Maybe it's compatible but I doubt that it will run in DOSBox since MS DOS utilities usually have a version check but you can try it.

I have to program assembler code applications for school on a 8086 in MS-DOS debug

I'd personally prefer to use an assembler and linker to write these apps since it is generally "complicated" to write them with the MS DOS debugger. 😜
It's funny if you have finished the app and you notice that you have forgotten 1 or 2 instructions in between 😁 .

You'll have to use the shareware ver of DosVer to use MS-DOS Debug in DosBox.

If you use Windows XP, you can find debug.exe from c:\windows\system32. It works in DOSBox.

Yep, he's right. Just tried it. Odd, Dos 6.22 requires dosver whereas XP's does not. Good info.