To a large extent, yes. This is what Putin & Co have been at least trying to do with the EU, NATO, and us. The weaker we get, the stronger Putin and Russia gets. And, unfortunately, Trump is helping him, although maybe not intentionally.
I'm not sure if that's their intentions. At least looking at the past few decades since the fall of the Soviet Union (and taking into consideration their entire history where they've mostly had to defend against invaders), their actions could be just as easily interpreted as defensive in nature. The West hasn't been exactly innocent in their dealings with the Russians, so if there's hostility between us, then we're just as much to blame as they are.
In some ways, if America and Russia forged closer ties with each other, it might even help both nations. Keep in mind that a large part of our problems with the rest of world have been indirectly caused by animosity between the U.S. and Russia. If not for that, then we would never have gotten involved in places like Vietnam, nor would we have any problems with nations like Iran or North Korea today. Other countries have taken advantage of the enmity between the superpowers, and both America and Russia have been worse off as a result. A friendlier relationship with Russia could actually strengthen America's position in the world.