Is it possible to use the tile texture as the source for normal (or bump) mapping?
Yes, as long as you don't need to batch render or GPU render (because Tile is not Arnold compliant).
I didn't try with the 3ds Max physical material, but that *should* work, it is just converted to an Arnold Standard Surface at render time.
Use it as a bump map.
The thing is, Tiles doesn't give you a normal map, Tiles gives you some colors. You'd have to convert that into a normal map, which would look something like this:
I had tried this also but it still does not produce the expected/desired results. This is with the bump height set to 100 (same result as with height at 1.0). I have tried settings of bump height over 2000 with no noticeable change.
Connect the bump2d to the standard surface normal.
In my screenshot, i had bump depth 1