I think they would win simply because they would have no qualms with completely wiping out the populace and after a continent gets glassed whoever is left would capitulate.
Yeah, but the point of the Astartes invading Earth isn't to "win at all costs", it's to obtain the demographic and economic power of the planet. Wiping out entire regions of the planet destroys both of those things. To put it shortly, nuking a planet you intend to conquer is mentally retarded. It's like trying to rob a bank, then opening with setting the money on fire.
The only reason you would go so far as to commit this widespread genocide is if you fear the political and/or military power of said planet and have no need for its demographic or economic resources. The Imperium will nuke a planet completely infested with tyranids or completely corrupted by Chaos, because the economic and demographic resources are already lost--and what remains is a political and military threat. Otherwise, they'd just start nuking any part of the planet that has any taint on it without bothering to send troops.
That's not to say they can't use orbital assets to assist in military campaigns--they can and would, but these would be mostly low-yield sort of stuff or attacking military targets or bunkers that are a threat, but not something the Imperium wants to capture for themselves. That really limits the sort of military utility that these ships provide, outside of logistics and intel.