Some external aspects, yes. Anything approaching actual puberty of the other sex, no.
Puberty blockers stop any puberty happening, they don't switch one puberty for another. But if given early enough they would, for example, stop the male facial bone changes that normally happen during puberty. So a boy would retain a 'boyish' face that is closer to a female one than that of an adult man.
Cross sex hormones (in either direction) will create a limited approximation of some secondary sex characteristics.
For example oestrogen changes fat deposits, making face and hips appear softer and rounder - but doesn't change underlying bone structure that has already grown. It also causes development of apparent breasts, but without full female internal tissue in the way of milk ducts etc. It does not grow any sort of cervix, ovaries, uterus etc. whatever David Lammy thinks.
Testosterone thickens vocal cords and deepens the voice, causes beard growth (usually somewhat sparse), increases muscle growth and can cause some additional bone growth (but again with limitations). It will enlarge a clitoris to look maybe a bit penisy but not grow a true penis or anything in the way of testes. And in neither case is it really a 'puberty' in any meaningful sense.
is it possible that they could possess functional ovaries or ovaries and testes that release hormones in the range to trigger female puberty?
There is a theoretical possibility that someone with a mosaic condition (essentially, cells from 2 different embryos get mixed up to create 1 baby) could have mainly XY cells, but have enough XX ones in the right place to produce ovaries. Exceptionally unlikely though - and the chances of them being functional are even smaller. Mixed up developmental signals from the rest of the body would cause havoc with their formation and function.
For someone with any of the normal XY DSDs, no. No functional ovaries. And testes are incapable of releasing the necessary types and levels of hormones for female puberty.