You pick up the LO frequency and offset the freq counter, and it will read the EXACT receive frequency.
I do not know about the $10.00 ones but the ones from almost all digital electronics have an adjustable offset (say 455 KHz) and a preamp that allows you to only need to get a wire close to the LO, no direct connection needed.
Here is one built into my homebrew receiver:
http://n2dts.smugmug.com/Ham-radio/i-MNgG3tR/XLSince it reads the LO frequency, it self corrects for drift, that is the display always reads the actual frequency.
You could use it on almost any old receiver, they make models to offset for ssb rigs, multi conversion, up and down conversion, etc.
You can get one in a small cabinet to sit on top of the receiver.