Actually the world in its current state could support everybody, but I don't want to get into that debate.
That's assuming pokemon are hostile, which according to the games themselves is not true. Most of the time.
Since we seem to assume the worst ITT, I'd assume by your logic a MAD situation which would result in no winner obviously. With Nuclear armaments, biological weapons, and nerve agents that kill every living thing they come into contact with I don't think people will go that easily.
Not with mass habitat destruction and overconsumption by first-world societies. Never mind the massive influx of a glabal-scale Pokémon population in addition to all the living creatures already here.
And- no- Pokémon are not portryed as hostile creatures- but they would need to compete with the pre-existing wildlife (and- consequently- us) for aforementioned food and territory.
Like I said, the only way it would work is if Pokémon have been there from the very start. If they just pop up outta nowhere, we also need to take into account the reactions from people who are not familiar with them. Again, as stated, these are immensely powerful creatures that we're dealing with here. You can't tell me that people are going to be wary (at the very least) around their new neighbours. If a Raticate smells grain in some farm's silo, it ain't gonna knock on the door and ask for it.
Also- never mind how long it would take for us to invent Pokéball technology. If Pokémon show up, they're all gonna be wild ones.
As for countermeasures, nukes and biochemical weapons are out right off the bat. No one's gonna be dumb enough to blast away half the countryside to get rid of these creatures. Those would invariably be an ultimate desperation maneuver, since those weapons do not discriminate. Conventional arms would only be effective against certain species. Any ghost-type is basically invulnerable to anything we got, and the numerous species with a shell, rock or steel skin are not going down unless we deploy the big guns. Keep in mind that they're more than apt to defend themselves.
This may all sound horribly pessimistic- but the chances of any good coming out of it are incredibly slim. If anything, the best Pokémon to introduce into the world would have to begin with Swalots, Muks, and Shaymins to start soaking up our pollution. Followed by Castforms or the Dragon trio to help regulate the weather and maximize production of agricultural lands by rerouting storms and eliminating drought. If various species were to get introduced slowly, indiscreetly, and strategically- things just might work out.
