Bribery, generals and disbanded armies

Are armies disbanded by bribe available as mercenaries if you have a general in the same province?

Loath as I am to pay for the same troops twice, I notices that a Greek faction member whom I bribed had a lot of mercenaries available to him immediately. It was incredibly expensive (the bribe alone was about 13,000 dinarii), but I gutted what was left of the Greek army, hired some excellent mercenaries, took a major province and got back about 3,000 dinarii from plunder. Now he's a four-star general who's taken another couple of provinces for me.

What i've found is. IF there are units in the army you bribe that you could build yourself, they will join your faction.