I think you might have some trouble with adding a team logo, even the name of the team, especially in a font that's even similar to the logo. Those trademarks are jealously guarded and you have to have a license to use them. I suspect you could use the logo and name of an amateur team without a problem, but you'd probably have to put the location on it if the team logo or name is similar to a pro team.
I can see a market for this. What about a sports bar or pizza parlor, would they use them for a team they sponsor? Making a batch of 20 to 40 for that market might go well, just engrave the name of the sponsor below the team logo. Doesn't have to be real beer, could just be root beer to cheer on the little or adult league team. There are lots of softball clubs around as well.
If you did this, you will want to have a number of jigs for the drill press, lathe and laser printer or other engraving device. It will make it easier to do and help you up production.
I see a nice hobby business working OK for spending money, and making a jig for drilling the hole, or a lathe, could be paid for out of initial profit. If you used a lathe, you could cut the opening to fit a metal or glass insert. Plastic finishing would likely be fine too. It's an interesting idea.