No, I think Suran had most of the military behind him. After the coup, we didn't see any Romulans fighting against the takeover -- not until later when it became clear that Shinzon was betraying them. Yes, the military nominally answered to the Senate, but that doesn't mean they couldn't plan treachery behind the Senate's back. History has its share of examples of militaries overthrowing their own governments. A well-known recent example was the 1999 Pakistan coup where the Pakistan Army and its chief of staff General Pervez Musharraf bloodlessly overthrew the elected government and instituted martial law.
A better example is what happened in Thailand just two weeks ago: the military becomes so disgusted by the conduct of their leaders that they basically sent them all to their rooms with no supper.
I always got the impression that the Romulan military (and also the Tal'Shiar) was a political institution unto itself, sort of like America's military-industrial complex, but with the added scariness of not having any sort of dependable loyalty to the government. I always figured that was actually the whole point of the military answering to "the Praetor" instead of the Emperor: The Star Emperor may nominally be the head of state for Romulus, but since he depends on the military to ENFORCE his government, he only has as much power as the Praetor allows him to have.
In that case, Shinzon didn't become the leader of Romulus so much as he became the leader of the military junta that had temporarily ousted the existing government. The Shinzon's junta had yet to appoint a successor government probably led to the power vacuum that Donatra hoped to fill, and was able to convince some of her fellow generals that getting rid of Shinzon would work in their favor when the new government was finally assembled.