First off, the direct answer to your question is "Yes", you can run some DOS 3.3 binary games without loading ProDOS
BASIC.SYSTEM. However, it isn't quite as simple as that.
Second point is that it isn't as trivial as wrapping the DOS 3.3 binary file as a
There is a big assumption here that by 'DOS 3.3 games' you mean single file games, e.g.
SYSTEM VOLUME 254
A 002 HELLO
*B 134 HARD HAT MACK
]BRUN HARD HAT MACK
On this, let me give you some more details.
While you can copy a binary file over from DOS 3.3 to ProDOS, I don't believe it will run by itself. As well, you cannot simply rename it to
.SYSTEM or set the file type since I believe there is some ProDOS header/magic that needs to happen (e.g. has to load at $2000 for one, if I remember correctly). As such, you won't be able to use the "bye" tool to launch Hard Hat Mack (HHM).
Some time ago, however, there was a developer who created something called DOS 3.3. Launcher which does the necessary tricks to get a DOS 3.3 binary like HHM to run under ProDOS. While it was intended for use under GS/OS, it does work fine under ProDOS 8 as well. It allows you to execute the
DOS3.3.LAUNCHER program with the full path to the "converted" HHM as an argument (through something called the startup protocol which is really just the full path with length/etc put in a particular memory location). It works well and is a key tool in many 8-bit games collections I've found these days.
Unfortunately, I'm not aware of an easy way to run HHM with the launcher from "bye", though presumably there are tools out there which could be configured to put HHM as the startup protocol argument.
So what can you do? You could write a simple system file for HHM which simply executes the launcher with the appropriate argument, but now you've got 3 files for the one game. Of course, someone could craft something a bit more custom to handle multiple games as well :-)
So long story short, you can run DOS 3.3 binary games without loading BASIC.SYSTEM, but you need to use DOS 3.3 launcher which needs help from another program (which could be in BASIC). In the end, does it really matter if you have to load BASIC.SYSTEM to do this?