Yes they can.
You are right that the cheap HTs don't have much of a useful meter (I own a couple). Two easy solutions are 1) body fade and 2) directional antennas.
Hold your HT close to your chest and turn around slowly, looking for the direction where your body blocks the most signal (the signal null). Now you know that the signal is coming from behind you. turn around, walk that way, rinse and repeat. The signal should get stronger.
Note that the null you are creating is rather shallow. At VHF/UHF frequencies, it can be filled in by signal reflections off of nearby objects. So try to avoid large buildings, chain-link fences, metal signs, etc. If you are not getting a good null, move to a clearer location and try again.
When the signal is so strong that you can't find the null, tune 5 or 10 KHz off frequency to put the signal into the skirts of the receiver's IF passband. If your hand-held is dual-band (144/440 MHz) and you are hunting on two meters, try tuning to the much weaker third harmonic of the signal in the 70 cm band while performing the "body shield."
Disconnecting the HT's "rubber duck" antenna will knock down the signal even more. Hearing the signal with antenna off is usually a "You are here!" indicator.
Fox hunting on 2m means there are a variety of simple directional antennas you could build that are also quite inexpensive. A 3 element yagi is a good choice as a small loop. there are several examples of yagis made from steel measuring tape, making them quite durable and easy to pack.
See the site http://www.homingin.com/ for lots of good information.