I know that the length of an antenna on a transmitter is critical. But on a 2.7MHz heli, being on the receiving end, does the length of the antenna make it better or worse for drop out of the signal?

Yes, antenna length is part of a " resonant circuit ", so even on receive a wrong length or untuned antenna will affect range.

It's been a while since I was into electronics, but iirc, here is the calculation method;
Cb band is 27Mhz (11m band), and since radio waves travel at 300,000,000 m/s, to find the optimum aerial length for cb you would use 300000000/27000000= 11. Hence the reason you see huge cb antennas.
For microwaves like our tx/rx (2.4Ghz) you would calculate 300000000/2400000000= 0.125 (12.5cm band). Hence the reason you see very short antennas on the latest technology.
Antennas can also be resonant and work on 1/4 waves, 1/2 wave, 5/8, et al, so a 1/4 wave antenna for 2.4Ghz would be 0.25 * 12.5cm = about 3.1cm
Hope this helps.

I used to do lots of repairs on radio equipment but I still know a fair bit about antennas, rf, etc..

As damo666 says, reciever antenna length is critical. But that's for optimum reception so, if you're flying at a distance, like outdoors, you need to let the full length dangle below your heli.

If you're flying close up, though, especially inside a house, you can wrap the antenna around a drinking straw (anything non-conductive) to make a neat coil and fix it to your skid or boom where it won't get in the way of anything. With my Twister Bell I lace it back and forth within the lattice tail boom a few times instead.