[dancing spawn of ungoliant]

I think that Grima didn't appreciate honour nor sincerity but was very fascinated by power and was eager to rule. That doesn't instantly make him a bad person but yet too easily seduced by slight chances to rise in rank. To Saruman that kind of people would have been too easy to brainwash. Saruman used Grima to gain his own goals but I tend to think that Grima acted willingly and knowing the cosequences.

In the book, after Isengard had been defeated and Saruman and Grima were just two vagabonds, Grima told that he hated Saruman and yet he didn't leave him. He didn't know how to live without his master anymore for sure a wizard had been a mighty ally before things started to go bad for them.
So, to the question: basically yes, that's possible.