well when he first encountered the ring, you have to remember bilbo still had it, so frodo must have had some admiration for it, when he got it, he was able to very easily resist its evil, except for when servants of sauron were in the vicinity, such as the encounter with the ringwaith, which nearly tempted him to put it on, when on weathertop about 5 nazgul were there right? or was it four, well together they did tempt him he put it on.
After this he had still in him a hard of the morgul blade which kept the evil of sauron near him, so the rings 'pull' must have become a little stronger, although in the fellowshio he is rarely tempted, it is in ttt and rotk where the ring really has an affect on him, that is because he is getting closer to mordor, so the ring is becoming stronger as it is nearer to sauron and the place of its creation, when the ring completely took over frodos will was the moment the ring had to be destroyed, in the place it was made, that ring must have been hell-a strong in there, it overwhelmed him and he claimed it,
so yes, the ring did have an effect on frodo, but not all the way through he wasnt immedietly gripped by it as isildur was....