There are a couple things going on. First as you've pointed out, the brushless motors of today are much more efficient than the old brushed motors. Over 90% vs in the 60's so basically a brushless motor is a 50% efficiency improvement. That alone will increase runtimes. Lipo batteries are also much more energy dense than nimh batteries and will last longer as well. If you have any inefficiencies, they will be seen in the form of heat.
The Ultima had 32 pitch gears which would have no issues with modern brushless motors. My concern would be your differential. That car has a gear diff unless you upgraded it to a ball. The original gear diff has only two planetary gears and they are a very soft pot metal such as pewter. These might not last long.
If you still have the original metal ladder style chassis where the battery sits across and out each side, I'd be concerned with battery terminal safety with a lipo battery. I'd be afraid of ripping one out if it got snagged on something. A graphite chassis such as on the later Ultima cars would definitely be better.
While these are concerns, I see no reason not to run the car. I love running vintage cars. Too many people today think old means junk or something that should be relegated to a museum somewhere. That's just not true. Have fun with it. Just understand it's limitations and any difficulties getting spare parts.