Word-Detective for 4/17/98 gives the following definition for "no-account".

'Meanwhile, on to "no-account." According to the Dictionary of American Regional English,
"no-account" is largely a Northeastern phrase, though its shortened form, "no-count," is common
to the American South. "No-account" means, of course, shiftless, lazy, dishonest, useless and
good-for-nothing, and can be applied to both animate beings (such as dogs and lawyers) and
inanimate objects (such as fuel pumps and brothers-in-law). It's a very handy term. "

The way I have always heard it used is to have a reputation for being lazy, etc. So it may be applied
unfairly to someone who merely happens to have no commendable achievements, though he may have actually tried hard.