After hearing Feliway suggested to others for a while now, I finally decided to actually do some research.
As far as I can tell... we don't know what Feliway actually is; we don't know what the "feline facial pheromone" it claims to replicate is (or if it even exists!); and if it does work, it might work through an entirely different mechanism than its creators suppose
If there exists a 'feline facial pheromone' that communicates to cats "this is a safe place", and if Feliway contains an analogue of said pheremone, and if your cat is deficient in producing said pheremone, then I'd expect it to help (but only for as long as your cat is deficient). That's a lot of "ifs" though...
Feliway ingredients basically include a solvent (ethanol or water), fatty acids (in varying proportions), an amine, and plant extracts. If you're up to reading through it, their patent is here: Feliway Patent
Note the "plant extracts", from Valeriana Officinalis L. to be precise. Valerian contains nepetalactone, the "active ingredient" in Nepeta, aka "catnip", so...
Incidentally, nepetalactone is apparently detected by cats via their vomeronasal organ (although I'm having a hard time digging up an actual study demonstrating that conclusively), which in where an animal detects... wait for it... "pheromones"
(1) Don't ever blindly trust a manufacturer's claims, or their explanation for said claims.
(2)(a) If Feliway contains some sort of "pheromone" analogue, it may work in the short term, but would be ineffective in the long term, except in the very specific case that your cat is deficient in producing something that Feliway actually replaces.
(2)(b) If Feliway's effect is because of the presence of nepetalactone, it is likely to be effective in cats that respond to catnip, but not in those that don't. In this case I could actually see it having a long-term effect. Note that this suggests that a (typically less expensive) catnip spray with a similar concentration of nepetalactone should be equally effective
(3) The contents of Feliway are relatively harmless (when used as per the instructions, of course!), so while you're exploring other options there's rather little harm in trying it and seeing if it helps.
Personally, I'd just suggest a slow introduction if you're worried about putting the two of them together.