[adouglas]

I'd mount the tires too. But here's some food for thought:

1) If you've never done a track day, your pace will be a lot closer to street-normal than flat-out. So the 501s, while not great track tires, would probably not hold you back if they're in good shape. Short answer is that you're not going to be pushing the bike very hard on your first day. It'll feel like you are, but trust me... you won't be.

2) Reading between the lines of your post re the previous owner, those tires (especially the rear) might be a bit squared-off. You may notice this, since you'll be spending a lot more time leaned over. It's not a big safety issue at beginner pace, but it's not ideal.

3) Check the tire manufacture date code (4 digits, first two are the week of the year and the last two are the year, i.e. 1405 is week 14, 2005). If it's more than five years old, time to replace the tire even if it isn't worn. But less than that, it's still got useful life. Obvious weathering issues like hardened rubber, sidewall cracks etc. trump this, of course.

4) Confidence is all-important and should absolutely be the deciding factor in whether you chuck serviceable tires or not. You may be riding no faster than you are on the street and completely within the limits of the tire but if you're not confident then your enjoyment, ability to learn, and safety all are seriously degraded. It's really important to remove anything that makes you nervous. This is one reason why I run warmers, even though the instructors don't. I know intellectually that within a lap my tires will be sticky. I know intellectually that I don't need warmers. But that nagging doubt about having a cold-tire crash is simply gone if I use them. That gives me mental capital to use on riding.