It can be a good and a bad thing. Mostly good but there are exceptions and circumstances.
Obviously your mood should be much better with testosterone use but sometimes hormones really bring your true self out...that's why people who are ass bags are sometimes bigger ass bags when they're supplementing. If you are really hurting from something, it may intensify it. Then again, it might not, it might be just what you need. It definitely should help with depression, but your mind will be more focused, and it would be possible to focus even more intensely on whatever it is that's bothering you....especially when you're dealing with an emotional loss of someone you may have loved. Even so, the odds should be in your favor.
All that said, sometimes when you're emotionally out, it's really hard to do things like train. For some it's a great outlet, but if it's a bad pain even training can seem like a brutal chore and it should never seem this way....if it does, it'll always be half-ass. If this is a really fresh breakup and you're wanting to jump on cycle, spend some time planning out what you want to do and get your gear in line, but allow yourself sometime to emotionally heal then go for it. If this is a truly bad loss, for you it may take awhile and you may still be hurting even after being on.
Good luck man.