Yes. It is not necessary for an out to be recorded for there to be an assist.
OBR 10.10 Assists
(a) The official scorer shall credit an assist to each fielder who
(1) throws or deflects a batted or thrown ball in such a way that a putout results, or would have resulted except for a subsequent error by any fielder.
(previously listed under OBR as 10.11)
(NCAA and FED are the same rule, but have slightly different wording)
An assist can also be credited on a steal attempt, even if the out is not recorded due to a muffed throw, if the official scorer believes that the runner attempting to steal would have been out had the throw not been muffed (the runner would be charged with a caught stealing; i.e., "2-E4 CS", or "2-E4d CS"). OBR 10.07(f)
The best way to look at it is like this: if the shortstop fields a ball, and then throws it to the first baseman, who drops it and allows a runner to reach base (6-E3, or as in my notation, 6-E3d), then the shortstop has done his job; i.e., he fielded the ball, and threw a catchable ball to first base that should have resulted in a putout. When figuring Fielding Percentages, this counts in favor of the shortstop.