Yes, of course. Source code would be nice, but I gamble on that there wasn't a terrible amount of bugs in that compiler. It is version 5.10, so not the first 5.x release, plus with the lack of good ways to distribute patches back then we all know software tended to be better tested. It also obviously works well enough to compile DOS 4.0 (and a bunch of user tools that are included) plus I have tried it already for some quite big code-bases without noticing anything being broken.
I feel like any bugs can probably be worked around and since it is C it is possible some things can be fixed by adding some macros in the include-files. I have thought of making some minor changes to the include-files to modify some of the few things I noticed that are missing from C89. I do not know if it is possible to make it 100% C89 compliant or if the binaries would have to be patched for that, but it seems like it already is 99% of the way.
* Since I can't comment on the comment to this post: Note I said C89. Definitely not going to go for anything more modern. Possibly add the standard integer size types from C99, as those can be useful for more portable code. There are other, bigger, compilers for more modern C versions that can cross-compile to DOS (and also Free Pascal that seems like a nice language for that).