Depends what kind of music you're talking about. (And what kind of bar, for that matter: nylon-string guitar playing solo Baroque repertoire in a wine bar? Don't think you need to worry about getting a board feed!)
But yes, decent external microphones will in almost every case be superior to the built-in mics on a Zoom handheld recorder. (And I only include the caveat "almost" because some folks have a very charitible definition of "decent".)
I do a lot of live recordings in bars using an OSS arrangement: two omnidirectional condenser mics on either side of a Jecklin disc. The whole thing only requires one mic stand (or one hanging mic mount), tends to image very well (no strange "holes" in the center), and works for everything from delicate classical chamber music to big band jazz to full-on balls-out raging rock groups with big PA support.
I just recently recorded a jazz trio using a totally ghetto (read: cheap) version of this...the
Zoom H4, a pair of Behringer ECM8000 mics, and a homemade Jecklin disc cobbled together from two old vinyl LP's covered with acoustical foam. While it didn't sound
quite as good as the recordings I've made with B&K condensers, a Josephson Jecklin disc, a Demeter mic preamp feeding a Lucid A/D, and a laptop DAW recording at 24/96, it was perfectly usable...and the band may even release these tracks on their next CD.
OSS rules!