No there's no consequence to ignoring a frozen cam in an eccentric BB if the chain slack (tension) is correct. In some cases it might get more frozen over time. The more serious issue is that your BB might get frozen into the eccentric, making maintenance or replacement difficult if not nearly impossible.

You can continue to ride it, or you can try to free it up now. The easiest way to free these if they're not too badly corroded is gently spread the shell a few millimeters by putting a place between the ears and threading the bolt from the wrong side so it presses the ears apart. (Edit, I just looked at the photo, and you're isn't a classic split shell with pinch bolts, so the preceding doesn't apply, I leave it there in case it helps someone else).

Then dolly the frame on a support that fits the frame's BB shell with clearance for the eccentric, and drive it straight across with a well placed hammer blow. Or, if you have a friend with an automotive shop, his bearing press is perfectly suited to this task, and will pop it free quickly and easily, probably with no damage, though you might have to buy a proper support ring.

Once the eccentric is out, clean it up with emery, and likewise the shell, then replace using grease or anti-sieze to prevent a repeater.