Can I just convert an IPF file to the ADF format?

You cannot convert IPF files to ADF. At least, it is unlikely the game would still work. It is pretty much impossible to do it and guarantee the game will still work.

Most copy protected games, any game with a Custom Disk Format, and even some non-copy protected (track loading) games will require extra information that the ADF file format does not provide.

The way an IPF stores the disk data is more like how a duplicator machine stores disk data when mastering disks. For instance, the Commodore Amiga has hundreds of custom formats for game disks. Publishing houses usually had their own set of disk formats they used, which were usually modified or added to.

Converting an IPF image to another format will most likely give you a non-working game, either very obviously, or by crashing in later levels.

There really is not any point in doing this.