Very much so, and there's a significant theorizing that Byzantine imperial iconoclasm had a profound impact on the codification of Islamic Law in the early Abbasid period. Because of the way in which Islamic Law came into being (i.e. the collective dominance of the religious scholarly class as a whole in a very decentralized way) it's difficult to trace these influences with any certainty, made all the more difficult because we can't really say for sure just how opposed to iconography early Muslims may have been because the documentary evidence is extremely poor.

One of the more interesting questions that results from that fact is that an equally interesting question might be how influenced was the Byzantine Empire by Islamic iconoclasm? Obviously the Byzantine empire had iconoclastic movements before the rise of Islam, but the religious scholars claim that Islam's opposition to human images was sui generis. The documentary evidence of this process is poor enough that it's hard to say if they're right or not.

While I think his work goes further in this theory than I'm comfortable with, see Benjamin Jokisch's Islamic Imperial Law for more on this.

Edit: This article, Islam, Iconoclasm, and the Declaration of Doctrine by G.R.D. King in the Bulletin of SOAS might be of interest. Here's a link to a pdf download it gets into much greater detail on the subject than I have here.