To be sure to get rid of all DNA I usually do both, but some say that it is useless, because one of the treatments should already remove everything. Still I think that to be sure its better to perform both..
btw: for solving RNA/DNA after any procedure, I used ddH2O or DEPC-H2O .. So I have no doubt that downstream applications might be inhibited by the solution buffer's ingredients
I know this is old, but I have done the same procedure as you did and electrophoresis in between,.. and guess what? Dnase from rneasy kit alone is not enough, you need both.