There's also a difference between the ovaries, ovulation/menstrual cycle, and eggs - testosterone will most likely discontinue ovulation and the menstrual cycle (from all reports) and maybe discourage the ovaries from continuing to make high levels of estrogen, but the eggs could still be perfectly intact. On the other hand, people with ovaries are born with all the eggs they'll ever have, so it's not like sperm; once a significant enough percentage of eggs are damaged, there's no way to recover them.
One warning : harvesting his eggs will require taking very high levels of *female* fertility hormones to promote super-ovulation. To the point that cis women report that it's uncomfortable/unpleasant to be on this sort of extreme hormonal regimen. I dunno how he'd feel about it...
http://www.mayoclinic.com/health/infertility/DS00310/DSECTION=treatments-and-drugs A quick poke on Google finds a number of sources like this one :
http://haveababy.com/fertility-information/ivf-authority/egg-quality-and-ovarian-reserve-effect/ suggesting that it's testosterone that is partly responsible for the decline in egg quality as a cis woman ages. Presumably, then, male levels of T *would* endanger egg quality. Honestly, if you're seriously considering it, the thing to do might be to call whichever fertility clinic you had in mind to use (because you presumably aren't planning to harvest his eggs yourselves, as that process also isn't as easy to do in a personal bathroom as sperm donation!), and ask how they think T affects egg quality? It sounds like a question that actually comes up with cis women and therefore one they might have a policy/theory on.