Yeah, my guess is he ends up with some ugly legal wrangling, but that his career isn't impacted all that much in the end. Here's a chunk from a Puck Daddy article about it:
An interesting twist to this is that domestic violence is a deportable offense, under Section 237 of the Immigration and Nationality Act.
Moreover, certain convictions for kidnapping are classified as “aggravated felonies” under Section 101(a)(43) of the Immigration and Nationality Act.
Therefore, if Varlamov is convicted of either, he may potentially be placed into removal proceedings by Immigration and Customs Enforcement.
My analysis, as a lawyer: I don't think he will be convicted or deported, because there would be a deal before it reaches that point. But I do think there's the potential for a civil lawsuit, and the arrest is a preamble to that suit.