Will I be able to keep this circuit on by routing the emitter to the base?
No, you can't do that. A BJT can't feed current from its own emitter back to its base.

If you want a latching effect, you need to create a bistable circuit with two transistors.







simulate this circuit &ndash; Schematic created using CircuitLab

Q2 and Q3 form a bistable multivibrator. C1 makes sure that the circuit powers up with Q2 off and Q3 and Q1 on. If the output of the current sense circuit ever goes high, it turns on Q2, which then turns off Q1 and Q3. Q3 being off makes sure that Q2 stays on until the power is interrupted.