Yes, you can get a good sound, depending upon the band.
 
Yes to the click track - it can make your (the engineer's) life easier, but don't allow that to kill the groove the band has.  THat is one of those band dependent issues.   Some bands play better loose.
 
Get the drums and bass down first.  Mic the drums (natch) and di the bass and guitarist, having them all play in the same room.  If they are a live band and studio virgins, they'll do better most likely playing together.  The key here for you is headphones.  You'll probably need a different room for the singer - many bands need one to keep track of where they are in the song.  Once again, this is the live thing rather than the musicianship of your band.  Not everybody can be a studio musician - that is why they get paid the big bucks in Nashville etc.  They ain't better, but they can hear/read the music once, understand the structure and not make mistakes at $1000s per hour.
 
IF you have separate rooms for miking guitar and bass, cool, but you'll still need headphones.  One particular home recording I had everyone bring their home mics and ran one off of a boombox.  For the bass, an ARt mp is cool.  It is a good studio/live tool.  Good preamp/DI that you can dial in starved plate tube (be careful, it starts to sound fluffy which may or more likely works).  It is a spitter, too.  For $50 a handy tool and great for live stuff at low end venues.
 
Overdubbing is the key.  IF they can't do that might as well stick to the live track version - just do the same thing but w/o the audience.  But most players can overdub their leads.  Also, live bands often don't understand that their distorted guitars won't sound "big" on CD.  Fuzzy gets small real quick, so most studio recordings have several guitars layered - playing different lines.  Not something a live 4-piece band can do, so they don't get it at first.
 
You'll have to play producer, too, I imagine, just not engineer.  Such as the layered guitars.  And figuring out the way to record their best performance.  You might get away w/ live gutiar if they need it and damn the bleed.  And remember a few well placed drum mics will beat a bunch of close mic'ed drums if the drummer is good.  I'd prefer bleed.  Most of the older stuff was recorded w/ lots o bleed in one big room.
 
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To do this.... if I were the one asked to record it....
 
You need 2 rooms.... run a snake between the 2 rooms, mic the band and give them a headphone or monitor mix for vocals....
 
Take the stereo out and record it. Do your mixing,  song by song....so you know where the leads and solo's may be.... unless you have the interface needed to do more than stereo.... and use cans to block out the sound in the room.
 
I did record a top 40 band a buddy of mine was in many many years ago in this manner. the medium was a TEAC 4 track that I owned at the time. The demo did turn out pretty nicely considering how we threw things together and used Peavey mics for everything into a Tapco board.