BEAD will put LESS tension on the neck, not more.
I have a Fender Jag strung BEAD. Zero probs. I didn't even need to change setup (YMMV), the shop where I bought it just ran the strings back and forth through the nut to make the slightest bit more clearance.
Second time this week, same question. Answer will be the same next week too.
(Somebody should sticky this)
Enjoy the lows!