Jim's right - if you can crack singing unaccompanied, you'll have got the measure of it. Not for nothing do those hideous talent shows on the telly make the contestants sing unaccompanied - it's the best measure of voice quality there is. If you can train your voice to hold a note and to work comfortably in a range (even a limited range - just pick your material carefully) then you've won 90 per cent of the battle.
Would that every would-be singer bothered to work on his or her voice, so go for it, Maggie.