Definitely not. We need to remember that although Act I scene 3 presents Banquo and Macbeth as friends and fellow commanders in Duncan's army, they are fundamentally different characters. The play in fact presents them as foils of each other, and this is shown very clearly through the way in which both characters respond to the prophecies they receive. In Act III scene 1, after Macbeth has killed Duncan and received the throne, it is clear that Banquo is very suspicious of Macbeth and does not feel any obligation to be loyal to him because of his belief that Macbeth killed Duncan. Note what he says at the beginning of this scene:
Banquo, as a just and good individual, feels no pressure to show loyalty to a king who has seized that position through ruthlessly killing his predecessor. The way in which he plans to run away with Fleance shows that he is definitely not loyal to Macbeth.