I agree with Tholian_Storm, the borg were once most feared and hated enemy. They have no central leader, thier unstoppable, and relentless. They made them so weak in every thing past TNG. Voyager, first contact, it's all same. Borg have no central leader, the drones act collectively, forming central brain ... so why they down size in perfection and get a central unit, that if it dies, the entire collective does ... that and vinculum is ugly. The only way federation was able to survive, was to send them computer virus. The only reason why the cube self destructed was because it didn't no how to combat the virus, and they didn't want risk infecting other cubes. Dominion would simply see the borg has invading force; just like federation. Another threat to the founder. They would start two wars, which they cant handle. They also made founder way way to powerful, the way they were shapeshifting is impossible, mass ratio wouldn't work out. Also, just becuase they take the form of some one doesn't mean their impossible to detected. On the topic at hand, the dominion would see the borg as a threat to founders, and would simply attack them both.
The borg would over run the dominion alpha quadrant forces, destroying or assimilating them. Then what was left of them,the breen and the cardassians would have ben thrown at the federation, probably destroying the federation. The romulans, klingons, and federation remnant would have made a death pact, and would have thrown every thing els at the borg. We would win, borg would be defeated ... again. Mean while the borg would have tracked down the dominion, and would evade and completely destroyed the dominion. The founder would most likely be dead or in hiding. The gamma quadrant would belong to the borg. The dominon hasn't encounter them before, they don't know how to defend against them. Ramming wouldn't help (tractor beam). Heck, we couldn't even defend against them with direct force(ever). We had to have picard be assimilated, and rescued, to give us a opportunity to send them virus that destroyed one cube out 100,000,000. (1 out of 100,000,000). Dominion dont stand chance. The federation had time to upgrade, but it didn't help much ... First contact. Look at all those upgraded akiras being blasted to bits. Heck we had ever since Q got bored, to upgraded. Did it help? no! Dominion are dead ...