I think it is tacky to do it AT the shower in front of the mom or bride-to be.
I don't think it is tacky to gather the addresses and help out the future mom/wife so that she has a list and can write them in her own handwriting at a later time.
I think that if you were mailed the invite to the shower, the host/ess should already have the addresses. If there is an unexpected guest or gift, the host/ess should be clever enough to discreetly gather the address for a thank you.
My reason: having the envelopes like that puts stress on the gift-getter to write them quickly. She should be able to do them in her own time, when she can, so that her thank-yous are properly thought out. I assume someone puts a lot of thought into buying a gift; the least I can do is put some thought into the thank you.
And yes, I know others are not as militant about this as I am and I'm okay with that!!!
For our wedding, DH and I had a spreadsheet of gifts, giver, addresses, and how we used/planned to use the gift. We had nice thank you's to send out and wanted to be good about it.