Can pyroclastic flows cross water?
In answer to the title question, "yes"!
Here are some videos from Montserrat Soufriere Hills where the phenomenon has been extensively studied (probably more than anywhere else):

http://www.geo.mtu.edu/volcanoes/west.indies/soufriere/govt/images/051296/

As well as Krakatoa, Mt Pelee's (Martinique) 1902 eruption managed to ignite ships in the harbour when the main town was destroyed - which suggests the pyroclastic flows crossed the harbour.

Also my u/g mapping area in North Wales included the Snowdon Volcanic Group. It and related tuffs appear to have been erupted over water and/or wet estuary type environments (there is open to debate).