Yes. The only real difficulty was having to lie on a table for a fairly long time with my legs in stirrups, and not moving them -- it is typical to leave the tube in place while the doctor goes and checks on the viability of the sample. In my case that took about 25 minutes. You can't move your lower body with the tube in place because you might jar it loose. (I took DH with me and made him talk with me for distraction while the doctor was out of the room.) As for the timing, the rule is between 10.5 and 12 weeks because that is the window when your are past the risk of possible resultant limb amputation, but before the cells that they will be harvesting deteriorate too much to be useful.
It's not clear from your post whether you are dealing with a translocation or deletion, and I'm afraid I don't know about whether or not FISH works for those. I was dealing with a trisomy, which FISH *can* detect very clearly. In any case, if a termination is at stake, I'm fairly confident in saying that your physician probably would not be recommending the CVS over an amnio if he or she did not think that you would have the initial results back before 15 weeks. (Also, the insurance companies often won't pay for FISH on a postnatal test unless it would make a material difference in the treatment strategy; if hurrying won't make a difference in the outcome, there isn't much point in paying extra for it or moving you to the head of the queue. When my child was stillborn the tests took eight weeks to come back; living patients who did not have a dismal prognosis naturally took priority at the lab.)
As to the NT test, I can only speak for myself and DH, but having dealt with a fatal trisomy before, we didn't want to fool around with tests that could not give us a definite yes or no answer; the issue of invasiveness was irrelevant. For us, getting the answer as early as possible and dealing with only one wait was tbe most that we were prepared to have to handle, because we really did not want to spend the bulk of the pregnancy dealing with the stress of not knowing for sure. (At the time I joined a support board for people who were dealing with this decision for this reason, and this seemed to be the general consensus there as well; most people opted to go straight to CVS the second time.)
For us it turned out well and we dodged the bullet that time; our healthy DD is nearly 4.