No, absolutely not. It must be prescribed. They often come in packs of two, so one can be left at school while the other stays with the child. (if the patient is an adult, one can be left at their work, or where ever they want it)
The school can't just have a random epipen - it must be prescribed for a specific child, just like an inhaler is prescribed for a specific child (usually kids with severe asthma have an inhaler at school plus one on their person). Actually, I have a friend whose DD has asthma, and she has them everywhere - lol. In her purse, her car, her house, the DD13 carries one, and the school has one.
Now I just keep one in my purse and one at home because either I'm at home or I have my purse with me! 
Next year a student coming into my grade level has a severe allergy that means there is a possibility that an epi-pen might need to be used. Apparently there is another student in another grade as well. The nurse is looking for teachers that are willing to get trained on how to administer the epi-pen, if needed, if she is out of the building or can't get there fast enough. I'm sure none of my team is going to volunteer and being the lead teacher, I will be asked. I understand the need, but I'm thinking that there is a serious liability surrounding this as well.
The way it was presented to us at our faculty meeting was that they were looking for volunteers. We have 5 teachers in each grade level. So no, I don't have to volunteer and it would not have any effect on my job. After speaking to the nurse at my school, I am the only one on my grade level that agreed to do the training, so the child will be put into my class. I have a teaching partner that is out on maternity leave, and she will need to be trained as well because we are departmentalized. The other 3 teachers will not be trained.
I have been teaching for 9 years now and I this is the first time that this has come up.
Yes, I would definitely learn how to use and be familiar with an epi pen. A few years ago, my 8 year old cousin died in the school cafeteria due to a severe peanut allergy and no teacher having access to his epi pen (it was kept in the nurses' office at the other end of the school) By the time teachers got him to the office, the nurse used his epi pen and EMTs got there but he was already gone. Minutes count in this type of situation, you do not have time to debate who will administer the epi pen.

Yes, I would definitely learn how to use and be familiar with an epi pen. A few years ago, my 8 year old cousin died in the school cafeteria due to a severe peanut allergy and no teacher having access to his epi pen (it was kept in the nurses' office at the other end of the school) By the time teachers got him to the office, the nurse used his epi pen and EMTs got there but he was already gone. Minutes count in this type of situation, you do not have time to debate who will administer the epi pen.

I just remembered that at my recent CPR/first aid re-cert the trainer had a pen that didn't have a needle. We were able to practice taking the cap off and slamming it on our own legs and other people's as well. Perhaps this might be able to be arranged for the teachers. It did help me understand how it would feel if I had to do it.

I work in HR for an educational nonprofit. This summer we have our first severely peanut/treenut allergic child. As soon as the health form came in, I gathered up our head of summer programs and our operations lead. In less than an half-hour we had:
1) A list liability questions from the realistic (What happens if we give the epi-pen and it isn't needed?) to the absurd (What happens if I smash the epi-pen into his artery and he starts to bleed out all over the floor?)
2) A plan for what we were telling various people involved
a) Everyone involved in the workshop will know how to administer an epi-pen, including the high-school interns helping out and where it is kept. We treated this -exactly- like we do firedrills/evacuation procedures "There's a kid who might need an epi-pen in your workshop - we're teaching you all to do it on date X at time Y.
b) workshop participants and non-involved interns will be told there's a severe peanut/treenut allergy, but not who it is, just that they can't bring nut-based snacks that week
c) non-involved staff will know there's a student with severe peanut/treenut allergies and will have the student discreetly pointed out to them. No nut-based snacks for staff, no opening the jar of PB you keep in your desk that week
d) every staff person knows the plan if there is a need to administer the epi-pen, and roles were assigned to keep the mass of interested bystanders under control and out of the way/make things run more smoothly - primary and backup
3) A list of questions for the parents to clarify if we needed to be more paranoid about our classroom prep (potential nut oils on the keyboard keys, mostly)
10 minutes on the phone with our liability carrier clarified that as long as we were employing the people involved in administering an epi-pen; -any- act they took and the potential negative affects thereof were covered. If we dropped him on his head while hauling him into the elevator and he developed swelling in his brain and died (we're a through lot!) then it was covered. And they were happy to fax me that clarification in writing.
The whole thing, including notifications/training people to use the epi-pen took less than an hour and was kind of a non-event.