Sort of. IBM really wanted to ensure that OS/2 had an imaging model that was compatible with what it used in some of its larger computers. This resulted in a bunch of differences between OS/2's imaging model and GDI. (Different window origin coordinates, etc.)
In a more Microsoft-centric world, I'm pretty sure the OS/2 API would've been exactly as you describe it and almost strictly in parallel with Windows. In fact, Microsoft did exactly this with Win32s (and Windows 95) In their relationship with Windows NT (which was once known as OS/2 NT or OS/2 3.0).
The same compiled binary could run on both the 'entry level' OS and the 'server level' OS, with a bit of care taken in the way the API was used.
In a more Microsoft-centric world, I'm pretty sure the OS/2 API would've been exactly as you describe it and almost strictly in parallel with Windows. In fact, Microsoft did exactly this with Win32s (and Windows 95) In their relationship with Windows NT (which was once known as OS/2 NT or OS/2 3.0).
The same compiled binary could run on both the 'entry level' OS and the 'server level' OS, with a bit of care taken in the way the API was used.