Answer
No, the LG leaving wouldn't form a resonance-stabilized carbocation.
Work Step by Step
1. Identify the leaving group:
- In this case, it is the "Br". (Normally, they are electronegative groups).
2. Analyze the carbon connected to the leaving group, and look if there is any double bond "next"* to it.
*Next: See if there is any double bond starting from the carbon next to the one we are analyzing, and ending in the other carbon (It can't end in the one we are analyzing.)
If there is any doubt: Start counting from the carbon we are analyzing, a "next" double bond is a bond between the carbons 2 and 3.
- In this case, there is not a "next" double bond, therefore, this compound will not be stabilized after the "Br" group leaves.