Yes, it is stalemate and it is a draw, but sometimes this is a critical point of the position! I can’t quite contradict Achernar (although I’m sure that stalemate has been forced on occasion with best play), but I can refer to one game that illustrates the theme:
In Chess Traps, Pitfalls & Swindles, I. A. Horowitz & Fred Reinfeld, ISBN 0-671-21041-6, the following position is shown:
White: Qc8, Bf5, Kg1, Pawns b7, f2, g2, h3
Black: Qd2, Ng6, Kh7, Pawns f6, g7, h4
which is Blackburne-Winawer (tournament and date not cited), with White to move.
The point of this position (Winawer’s last desperate attempt to save the game) is:
1 b8=Q?? Qc1+!!
2 Kh2 …
(if 2 Q:ci, then stalemate)
2 … Qf4+!!
3 Kg1 …
(if 3 Q:f4, stalemate.
if 3 g3, then 3…Q:f2+ and draws by perpetual)
3 … Qc1+!!
and black draws by perpetual check.
Blackburne actually played 1 B:g6 and Winawer resigned. The punctuation above is from the book: I would agree with the “??”, but award a single exclamation point solely to black’s first, not “!!” to all three moves.
The motif does not come up very often in master play - problems are another matter - but is a very beautiful subtlety when it does.