Yes.

It is possible for your body to prioritize loading more strongly on one side than the other without you being aware of it. The grip connection is a good point that I never thought of.

Unfortunately, it is also possible for your chest muscles to be genetically assymetrical. When you train it just becomes more pronounced. I still suspect you can even them out in this case.

I have no idea if this is a good idea; it is just something I have heard of:
Uneven barbell loading. Purposely putting a little more weight on one side. Sounds dangerous, but you'll be expecting it.

A slight difference, say 5 pounds, will make it feel like the majority of the load is on your week side. The trick would be to concetrate on bringing the bar up completely parallel, never letting it dip on the weak side.

This could also help "train" your body away from the uneven priority in load if that is the case.

I've heard of this on things like presses and barbell curls. NEVER on squats or deadlifts.

Again, this is just something I've heard. I've never tried it. The others may have some info or opinion on the practicallity of this.