Can't see what the pickup is in that tiny picture - is it a bridge pickup? Then you'd still have an Esquire.
Adding a neck pickup would make it something else.
EDIT: Ah, never mind - I see that BG1400 is the pickup model, not the guitar.
Noiseless stacked Tele bridge? Yah, still an Esquire IMO.
Have never heard that model myself, even in demos.
I know Reverend Billy likes pretty fat tone.
EDIT (again): WOW, wound to 29K? That's gotta be a beast! Hope you love it.