yes, but it would have a terribly twr, and I couldn't get my apoapsis out of the atmosphere
The TWR is 1.3, it's a little low but not that bad, and your core is more durable. Have a look:
This is after booster separation:
This is once the core is depleted:
My apoapsis is still slightly below 30 km, but I'm very close to the objective. In the end...
See, I reach orbit with a very decent fuel quantity in stock.
Just make sure you raise enough your apoapsis while you're running on the boosters, then it will be fine. Sincerely, that rocket is pretty good.