A popular band can,
if there are good sources for the information. Regardless of what other policy exists, having written a number of band articles, I've found that to be more or less the one de-facto rule: cite thy sources, preferably to sources that seem relatively legit (musicological books or journal articles good; newspapers and magazines ok; the band's own website ok but not as the only source; "personal communication" not so good). Overall I think that makes sense, because it's the only real way of verifying that it's not just fans writing impossible-to-verify opinion or lore. Plus, Wikipedia is supposed to be a tertiary source that compiles secondary sources, which doesn't make any sense if there aren't secondary sources.
Whenever I've written articles about music groups that do have good references, I've never run into problems, even if they're obscure groups. For example, I recently wrote one on a minor 1980s punk band, with citations to the book American Hardcore (a history of 80s hardcore), which I doubt anybody would challenge. I do think there's an awkward gap around subjects that clearly should have secondary sources, but for some reason don't, because music historians and journalists have somehow neglected to write about them, or just haven't done it yet (musicology tends to lag). I can see why people get pissed off in those cases, but I do think it's basically no-win for Wikipedia, because in cases where good sources don't exist, it's not possible to produce an article up to what Wikipedia claims are its standards, a tertiary-literature article solidly referenced to the existing literature; because the problem is with the secondary literature itself being deficient (http://www.kmjn.org/notes/wikipedia_notability_verifiability...).
Nowadays I mostly do my Wikipedia-editing source-first: I find a good source or two about something, and then decide, hey, this is a good basis for a Wikipedia article. So for example, I'll pick up a book on the history of hip-hop, and use it to write articles about hip-hop musicians. Doing it that way, I have a remarkably laid-back, trouble-free Wikipedia-editing experience. It's still theoretically possible to read some policy pages in a way that could cause me problems: there might be some minor band that I've written a well-referenced article on, but is somehow still "too minor" to deserve a Wikipedia article under the Notability policies. But in practice, those objections almost never come up in the case of well-referenced articles; I think Verifiability basically trumps Notability these days, and that the deletionists who argued for a more strongly curated encyclopedia have lost that battle.