They could perhaps be modified to do that but the baseband firmware is usually very closed source.
There is only one example I know, there was one particular dumbphone from the 2G era for which the baseband sourcecode was available due to a hack. You could use several (one for uplink and one for downlink) of these with modified firmware to sniff 2G traffic. I forget which model it was exactly but obviously the price ballooned on eBay :)
Haven't heard of this happening with later models. Baseband sourcecode firmware is really rare.