No. EDB is not a static analyzer and actually requires the host OS to be able to load and execute the code. From there, EDB will debug that running process. Since Linux cannot run Windows executables, neither can EDB.

It is possible that limited success can be achieved by running the target application with wine, and then debugging the wine process that is hosting the Windows executable... but I don't expect that to be a very pleasant experience and is not really a "supported" use case.