Whether it's worth it or not depends on what you want to do with it, and what you expect to get out of this character. It's impossible to answer in general, but I can answer your specific questions.
Also wondering how long does the training take,
A very long time to get proficient enough to do risky things. You're looking at many RL months if you find a situation where you do nothing else full-time; probably closer to a year if you do it on the side. Of course, if you're willing to take risks you can do things before that.
how much gold does it cost,
A lot; then again relatively not so much considering how much gold there is in the game. Training 6 hours a turn will cost you 336 gold a week once you are the expert level; a region Lord can be able to rake in that gold.
and can you still do other things, like maintain a unit and go into battle?
Yes! You get a limitation on unit size, but especially if you're able to maintain your H/P level they are reasonable.
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