Have you experienced them, or are you just worried about them? Everyone's reaction is different, so don't assume the worst (though do be prepared, just in case).

I had occasional weepy moments for the first few months on ADT and Apalutamide (having what I though of then as a "terminal" cancer diagnosis, and being paralysed in a hospital bed from the tumour's spinal-cord compression didn't help matters), but then I got used to it, and even at the start the weepy moments were relatively rare.

I never lost mental sharpness — even lying in the hospital bed, I was able to fix problems on a web site remotely via a terminal emulator on my phone (I couldn't sit up to use a laptop yet) and could solve a sudoku. That said, I do need to rest a bit more these days, and work only half time now (I'm lucky that I had private disability insurance).

Your mileage may vary. ADT may be horrible, or it may be a mild treatment that gives you many more years to enjoy life, as happened for me.