If the pads don’t come back and bite the disc, or they feel spongy, you have air in the system. Bleeding will then be necessary.
Bleeding isn’t a that trickier a task, but you have to be careful not to get fluid on the pads or rotor.
Each brake should have a set amount of fluid. If there is too much, it may work fine for a while, but depending on whether it is an open or closed system, will present binding issues – especially when the brake gets hot. If it does, put a length of bleed hose on the bleed nipple and loosen to allow about a quarter of a lever pull’s worth to flow out. Re-tigthen without letting go of the lever, put a rag round the pipe and make sure no fluid spills when you remove the pipe. If you want to go belts and braces, after locking off the bleed nipple,drop the wheel out, remove the pads before removing the bleed hose. Test ride and see how it behaves. I have done this in the Alps several times. It’s when you get fluid heating up that you get trouble. Long decents cause pump up (heating of the brake fluid), hence why I have had to fix several of my mate’s bikes as well as my own. Use DOT 5.1 fluid if you intend doing any Alpine Downhill runs.
The other issue is that you might have a loose wheel cone. This will allow lateral movement of the hub and can cause light rubbing and “chinging” noises of the rotor when cornering.