you are correct that voltage is voltage, most things don't care if it is voltage from a lipo, nimh or PB for that matter... but...
three things to look out for:
1) fully charged voltage for lipo is actually 8.4v, so verify that the ESC(s) built into the tamiya tank controller and the other electronic bits can safely handle that.
2) the internal resistance for lipos is much lower than average nimh, so a lipo can dump more amps into the esc, which may cause it to overheat... and cause a thermal cutoff... if the tamiya electronics don't have a thermal cutoff, PLEASE get rid of the cheap white plastic tamiya connectors... they are only rated for 10 to 15 amps, and will literally weld themselves together.
3) the low voltage cut-off for lipos is 3.3v per cell, so for a 2 cell pack, that would be 6.6v, if you go below 3.0v per cell, you most likely have destroyed the cell, and it is useless. most brushed ESCs do not have a low voltage cutoff, or it is set for nimh - a voltage below 6v, so you will want to buy a low voltage lipo saver or lipo alarm to make sure you don't kill your lipos by discharging them too far. you can find lipo alarms for under $4.00 on ebay