We don't know how many were killed in the Dominion War. I can only recall three figures given in the show.
*800+ million Cardassians on Cardassia Prime killed by the Dom at the end of the war.
*1,600-odd Starfleet casualties in a casualty report at the end of Siege of AR-558.
*7 million Cardassian military casualties from the start of the war to when Damar rebels.
I doubt anyone will take the war into the Gamma Quadrant after the Dominion. They have no support on the other side and they know very little about the size of the Dominion or the location of the Founder's homeworld. The wormhole is unreliable since it can be closed on the whim of the Prophets. The Klingons got battered badly at the end and I think Sloan said it would take them over ten years to get back up to full strength. The Romulans joined 6 months into the war but in the two battles we seen them in they suffer heavily and we know that holding Chin'toka cost them heavily in early season 7. I doubt either of them could hope to conduct a serious war with the Dominion on their home turf.
As for Dominion attacks they seem to honour treaties pretty well, so in the short term I think they won't attack. In the long term it would take a serious change of mindset where the Dominion no longer believes that they need to exert their will over all solids to be safe.
Given how the war ended I doubt many people would be willing to join up with the Dominion like Cardassia did and given the proven unreliability of the wormhole launching an invasion is very risky if not impossible. The way around that would be to develop drive tech like slipstream, transwarp or coaxial so that the 10,000s of light years between the Dominion's heartland and the Federation can be easily and quickly traversed. The Dominion is running out of time since in 200 years the Federation will be making use of time travel as a standard instrument, once someone conquers time travel technology attacking them in a conventional sense is a very, very risky prospect.
