In such a situation, first-strike bonus ability (or simply attacking first) might come somehow handy!
No.
First strike super ability means your opponent doesn't fire back-but only if you destroy them in the first round of combat. Since we're dealing with 1 firepower ships in this example, you'd need to be using cargo hulls, without hp modules-and so would your opponent.
Secondly, GCII does not do "attacking first", after DL (I believe DL in its entirety has the attack first system, but it may only be up to about 1.3-someone who still plays DL can enlighten me, and the rest of us).
Regardless of whoever "fires first", in GCII DA & TA (and possibly late DL, see above), the defender fires back even if they are destroyed in the first round of combat...except, as stated above, for the first strike super ability.
To recap: No.