Maybe
What do you mean tuned to a specific band? As in like the 10 m band or something?
If you mean just scan a range of frequencies, you can do that with most scanners.
If you mean bands like "FM Broadcast", "AM Broadcast", "UHF TV" or something, a fair amount of Unidens do scan like that, in their "Service Search" but most of the older scanners and cheaper scanners don't have those features.
A good idea to do with your scanners, since I am looking for some older ones, would be for you to put them in a box and ship them to me. LoL
Anyway, I think a good idea, at least what I like to do is, use my nice scanners for searching and discovering new stuff, but use an older scanner, just to do that stuff like monitor local police and stuff, because, my police/fire/ems only use VHF and UHF, so I don't need a $200+ scanner to hear them but if they ever switch to trunking here, I can't go with the old and cheap. This may not work for you depending on your location and what emergency services use in your area.