ehh not really as long as it is a 2S I'd say any brushed ESC made in the last 15 years would be find with the slightly higher voltage as I've ran lipos on plenty of old brushed ESC's. My crawlers all only ran lipos, and the newest ESC in those I think was made in 2012.
Now the cutoff is the issue as old ESC's don't have it which in this case a cheap Low Voltage Alarm would work(what I used in my brushed vehicles) that you plug into the balance port, and it makes a very loud annoying buzz sound when a cell hits I think 3.8 volts.

The only other issue I see is it is a Tamiya... their ESC's kind of suck as some lack BEC's, and pump full battery voltage into the RX, and servos. I know the Tamiya TEU 104BK does this and needs modifications, and a cheap part to not destroy radio equipment(I've done it) I'm not sure about other Tamiya ESC's though, and do know some built in BEC's.