Sorry, but signal to noise ratio (SNR) is a key parameter for any communications link, whether it is analog or digital (such as ATSC). For analog reception, poor SNR leads to a snowy picture. For digital reception, SNR greatly determines whether the transmitted packet is in fact a "clean" one or an "unresolvable" one.
Taken by itself, the clean/unclean packet ratio's effect on reception is only a function of the receiver's error correction loop. This is typically similar receiver to receiver since the error correction is part of the communcations protocol. Actual receiver performance is keyed to symbol recovery, which is influenced by SNR and multipath.
A preamp is useful for low level signals provided it has a low noise figure, so not just any amp will do. In the worst case, a poorly chosen amp will degrade the SNR, and give poorer reception no matter how much gain it has.
So long story short, you can get good reception results with relatively low signal strength, as long as your SNR remains decent.