Yes, only some more exotic disk routines may have some compatibility issues (ie CP/M set track, select disk, sector translate and read sector commands do just nothing or return error), but normal CP/M programs should run just fine with MSX-DOS. If there is possibility to select terminal emulation, you should select VT52.
The real problem is that msx1 has only 40 columns, where 90% of the old cp/m programs ask for 80 columns
Apart this, provided that the program does not use exotic disk routines, you have also to copy the cp/m files on msxdos disks (the file systems are different)