The Army doesn't care so long as they get lots of gadgets and get to stomp on neighbouring countries, the NSDAP doesn't care so long as the lower blokes get to smash up Communists and Jews and Romani, and the upper blokes get to drink fine wine and lounge in plush chairs with French paintings all around.
Well sort of. The problem is that the Army might not get its fine toys under an SA regime. Roehm's plan, as far as it can be discerned, was a more Swiss style militia or possibly a levee-en-masse army. So tanks and other toys would likely be sacrificed for the sake of infantry. And far worse, Roehm would insist on the officer corps integrating with all the Sub-Upper Troop Leaders or whatever goofy ranks the SA had. Roehm's plan was not to make a paralell organization like the Waffen SS. It was to combine the army and the SA. That means threatening the army's position in society. The generals might have wanted the Storm Troopers in their ranks as soldiers, but they didn't want to share their officers mess with a bunch of street thugs.
Direct involvement of the Army may not occur, though plenty of generals were involved in manipulating politics to their own advantage. The Party was interested in staying in power. That doesn't mean that they had an interest in keeping Roehm in power. Below the Fuehrer was a lot of mindless backstabbing and intrigue. And Hitler had been too disinterested in the minutae of administration to keep the members in lockstep or even encourage them to work together effectively (A definite distinction between Hitler and Stalin).The Army was too spineless to mount a coup d'etat, and the Party was too self-interested. Fuhrer Roehm would have happily trundled along bollocksing things up, getting Germany into losing wars, etc. There'd be somewhat less of a cult of personality about, giving Nazi apologists and Panzer fans less chance of saying, "no, no, it was just that crazy Hitler... otherwise there'd have been no mass murder and the Germans would have won. Really!"
Once Hitler is gone, I don't see every party bigwig swinging their loyalty to Roehm. At least a few of them are going to seek support from the non-party conservatives, industrialists, and the military. If a civil war or counter-coup doesn't happen, Roehm is going to spend years purging the ranks of society. Which would at least delay the start of the war unless Roehm is even more out of touch with reality than Hitler (not saying that isn't a possibility).