Yes, you could.
Some WHDLOAD installs are compiled to run at 020 as minimum, some require rare 010 for so called VBR support which you cannot get on plain 68000.
I have found at least 2 games from my personal interest (Amiga Karate, F/A-18 Interceptor) which failed to run on configuration similar of your own. The issue was resolved as slave/install author was kind enough to re-compile stuff compatible for 68000. However, I find that a rather exceptional case, not a common among a niche of WHDLOAD slave/install authors.
At the end, at least you got one more reason to start over getting A500 accelerator.
Or switch to A1200 which is, hands down, a WHDLOAD gaming champ, right from bootstart.