If the band isn't used to playing with and recording to a click, there are really only a couple of reasons (that I can think of why) you'd even suggest they start doing so "now" (as in, while they're sitting in your studio waiting to record):
1 - They're expecting you to edit the drums. If a band is expecting you to edit their drums (or if you're expecting you'll have to edit them in order to end up with anything resembling a listenable recording), you're likely going to have a pretty awful time trying to do so without a click/grid. Editing guitars/keys/vocals should really be done to the drums either way, regardless of what the click's telling you.
2 - They have large sections where the drums drop out. Unless they're freeform in nature, you'll want to at least be able to turn on the click for these sections, so the other instrumentalists will have something to play to, especially if there will be more than one track/performance during the drop out (eg: two acoustic guitars and vocals, or something of that nature).
Either way, to click or not to click is definitely something you should work out with the band beforehand, so that they're prepared. If they're expecting to record to a click, you need to get tempo maps from them (how many measures of how many bpm). 99% of the time, these will be at least a little off, but it will create/build awareness within the band of the tempo changes, and will at least get you in the ballpark once they come in. Plus, it teaches them an incredibly useful skill that any future engineer (possibly yourself) will certainly appreciate.
As a reasonably competent non-drummer musician, I can't really fathom not being able to record to a click, but there is definitely an art to it as a drummer. Even competent drummers with good internal rhythm can have trouble getting the right feel with a click without some experience under their belt.