They don't seem that involved in the creative process of incoming talents who've made it elsewhere. The appeal of hiring a big indie darling on a stage like ROH is keeping what made them special and worthy of signing in the first place. Guys like Brody King, PCO, Bandido, Dalton Castle, Marty Scurll, and Rush had their gimmicks before showing up in ROH, and if you booked them outside of ROH you'd get the same characters. The appeal of having them and using them for a company like ROH would be to put them in dream matches or feuds, and to put them in different booking situations than what they'd encounter elsewhere. You don't mess with the character, you mess with the circumstances surrounding it. I doubt anyone has outright creative control, but they probably do have more say in how their character is used than a wrestler would in WWE, because unlike in the WWE the wrestler's reputation with the fans is what draws viewers in.
You also have to consider that ROH is in cahoots with other promotions that are by all means bigger than they are. CMLL is huge in Mexico and New Japan is THE promotion in Japan. CMLL probably has rights to many of the lucha personas that grace ROH and New Japan's airwaves, and New Japan has so much control over their wrestlers that they can tell them how to wrestle. ROH definitely doesn't have big pull over those talents, and I doubt they have as much pull over their own talents as CMLL or NJPW have. You screw up in Mexico or leave the territory and you lose your identity in a place like CMLL. Someone else gets to wear your legacy and represent your heritage and use a name that your family's built up for decades to make themselves and CMLL money. ROH definitely doesn't have that kind of control over their talents. There can be more than one Mistico, but there can't be more than one Jay Lethal, although I do wonder if they own any I.P. over talent names these days. I kind of doubt it.
I get the vibe that ROH does have more creative input and control over trainees because they're unproven commodities that have nothing to lose from listening to ROH. Once their talent learns the ropes and gains a following, I'm sure ROH might have to worry about them going elsewhere. They kind of always have had that problem..