according to that definition, Gilly can not be counted as an all-rounder!
Of course he can't. Gilchrist was a wicketkeeper-batsman (or probably more accurate to say batsman-wicketkeeper), not an all-rounder.
BIG difference.
Anyway I've always said that an all-rounder is someone roughly equal in batting and bowling skill. Khaled Mahmud
was an all-rounder, he just wasn't (by international standards) a very good one, same way Anwar Hossain Monir wasn't a very good bowler and Mohammad Ashraful isn't a very good batsman.
The very best all-rounders would indeed be good enough to play Test cricket purely as either bowler or batsman, but such all-rounders are exceptionally rare. All-rounders good enough to be in their country's top-five batsman list and top-five bowler list might well be virtually unheard-of.
Imran Khan between '80/81 and '88/89 might, just, have been such a thing for Pakistan. But it'd be hard to say conclusively that he was better with bat than all of Javed, Zaheer, Majid, whoever else was playing at the time. Clearly with ball he's better than any other Pakistani.
Likewise was Botham of '78-'84 really one of the best batsmen in England? Possibly, but can we say for sure he was better than Gooch, Boycott, Gower, etc.? No.
Sobers is about the only one who might qualify, from serious Test teams of the 1930s onwards. Even Keith Miller must've been precious rarely among the best batsmen in his teams, given they contained the likes of Barnes, Morris, Hassett, Bradman, Loxton, Harvey etc.
Sobers, BTW, was most certainly one of the best four bowlers in West Indies between, perhaps, '61/62 and '73. Before then he wasn't much of a bowler. And clearly he was THE best batsman in West Indies between '58 and '73. He's perfectly possibly the best batsman in West Indian history.
I suppose Kallis of '97/98-'03 or so might, just, qualify.
I think the question posed is an unrealistic one. World-class all-rounders, who are good enough to play Test cricket as batsmen and bowlers simualtaneously, are exceptionally rare: Hirst, Noble, Miller, Sobers, Imran Khan, Botham. Even Kapil Dev doesn't even qualify IMO - who seriously thinks that, at any point, he'd have played for India purely as a batsman given the wealth of quality batting they've virtually always had to choose from?
Test-class all-rounders and World-class all-rounders are different things. Jacob Oram and Andrew Flintoff are the former; precious few have ever been the latter.