Yes, no, maybe so. You can buy strings willy-nilly, paying no attention to tension, and end up higher or lower with BEAD versus EADG. For example the D'Addario ProSteel EPS180 EADG string set runs (String, Gauge, Tension in lbs):
G____0.0350____45.200
D____0.0550____33.850
A____0.0750____34.490
E____0.0950____30.810
Whereas the bottom four strings from the ProSteel EPS160-5 BEADG set runs:
D____0.0700____54.180
A____0.0850____44.170
E____0.1050____36.670
B____0.1350____33.240
Every string in that BEAD set runs higher tension than the equivalent string in the EADG set. You can get the tensions you like in any tuning within reason by doing your homework. Only a few string makers (D'Addario, Thomastik-Infield, Circle K Strings) publish the data you need but you can get a wide variety of strings from those three. D'Addario supposedly is offering all its strings as singles starting some time this year, if not already. Talk to BassStringsOnline.com about that. Some TI singles are available from the same source. CircleKStrings.com offers a HUGE variety of string gauges in their one line of roundwound strings and you can make your own set by picking and choosing. They even extend the top end of their offerings with a nice selection of light gauge plain strings if you have an ERB or want to up tune.
Ken