The entire ship is already at red alert by the time of the ramming. This is after two Romulan Birds of Prey came out of cloak and joined the Enterprise in attacking the Scimitar. The entire crew is at battle stations, with parts of the crew searching for the intruders that beamed aboard. As mentioned in What does the non-bridge crew do during red alert? there are civilian shelter points throughout the ship. The outer rim of the Sovereign class ship like the Enterprise-E is mainly composed of crew quarters, which under red alert, would (should) be empty. I refuse to believe Starfleet Engineering would not take this into account in ship design or battle protocol. Any basic design would keep personal and critical systems as protected as possible.
That said, Picard would not so callously ram the enemy if people were there, unless it was the only solution, unless it was dire.
LAFORGE: It's called a cascading biogenic pulse. The unique properties of thalaron radiation
allow the energy beam to expand almost without limit. Depending on the radiant
intensity it could encompass a ship, ...or a planet.
PICARD: He could only have built a weapon of such scope for one reason.
He's going after Earth.
TROI: How can you be certain?
PICARD: I know how he thinks.
RIKER: Destroy humanity. You cripple the Federation.
PICARD: The Romulans invade...
RIKER: No way of penetrating his cloak?
RIKER: So he could pass within ten metres of every ship in Starfleet and they'd never know.
CRUSHER: We do have one advantage though. He needs your blood to live.
He might come after you first.
PICARD: I'm counting on it. We've been ordered to head to sector ten forty-five.
Our fleet has diverted to meet us there.
RIKER: Strength in numbers?
PICARD: At least that's what we hope.
...He must not be allowed to use that weapon.
All other concerns are secondary. ...You understand me?
RIKER: Yes sir.
PICARD: All hands. Battle stations!
The impending genocide of Earth's population would merit that call.