I came across this question myself and there is no possibility to get an spsitedataquery from client object model. 

What I did was writing a short webservice myself which did an spsitedataquery and queried this webservice from client side.

Reference:
https://msdn.microsoft.com/en-us/library/ff798388.aspx

And this question has already been asked:
https://sharepoint.stackexchange.com/questions/7206/client-object-model-equivalent-of-spsitedataquery