The common name for that bar is the "dock". And as for your question regarding getting the height of it through the Android API the short answer is no.
Longer answer, each home screen replacement app and possibly each theme used within that app defines their own "dock" if any. You would have to write solutions for multiple possibilities (an example of some popular ones can be found here). You could cut the list down to the default apps used by the most popular ROMs installed on the most popular phones and some may even have APIs or ways to access their settings but you could never cover every case and would have to maintain your code against multiple other apps' updates.
Alternatively you could redesign your wallpapers to assume an average height obscured and not include too much detailed content in that lowest portion of the screen. You could even offer two versions of each wallpaper to the user. One with the buffer for a dock and another without; let them choose which suits their theme best.
Even if you could access the height of a dock across all homescreen apps 100% of the time you'd still need to know whether it is transparent or not, contains app icons and does in fact obscure your wallpaper. Some apps allow the user to toggle the dock between hidden and visible states and thus may be active but not actually covering your wallpaper.