Are there any compatibility issues between an HP printer and Canon photo papers such as glossy plus?

While I haven't seen any quality issues caused by using HP paper in a Canon or the other way around. Nor have I seen print quality problems with Kodak paper.

I have seen print quality problems caused by poor paper quality or misaligned print heads. By far the most problems I've see are caused by human error. Selecting High Gloss paper when there is actually Matte finished paper in the printer.

You should be fine.

Each manufacturer formulates their papers to work specifrically with their inks. While this doesn't mean you have to use the same papers it does mean you WILL get visibly better results when you match the ink and the paper.