I would worry about it because you're not getting much clamping force from the lockdown nuts. Does adding one chain link really cause tire rubbing up front? A different gear setup you could use that would allow you to move it back into the dropouts a little further?

 

Some pics below so better show what I'm dealing with. You see an IGH hub but the principle is the same as SS and the front wheel is actually a singlespeed hub (so I have a backup drivetrain).

I added 2 links of chain to pull the tire back to the "sweet spot" of the rear triangle. With the chain shorter, the very outside nubs of the tire rubbed on the chainstays. Trimming the nubs down with a razor blade would probably solve problem; I just hate taking a knife to new rubber and the nubs are not that tall to start with.

I suppose another option would be to use a half-link.

 

Based on your picture and type of lock nuts, I'd be OK riding as is, but once you need to add any tension to the chain, I'd question it. Do you have any other chainrings one tooth smaller or cogs one tooth larger you can try?

Will this also be an issue with the front tire?

 

Looks fine but you will run out of room as the chain wears in. Would try adding a half length to give you more adjustment options.

 

Since you are running gears, I would not worry since you won't be laying down any serious torque like on a real bike. I meant single speed. Seriously though, I would just try it. If it doesn't work, you do have that front hub.