We've seen them call for back up.
But you're right, they'd probably never straight up run away, but they could hold position and not engage or decide to go and proctect the civilians. It's good for the marines to know where an emperor is sailing but it's not good for them to loose a couple of ships that simply run up to them. And I doubt that many vice-admirals would just charge into them if they knew they were unprepared.
Like when Momonga went to meet Boa Hancock, he wasn't there to fight so we just see him holding his ground. It's was a different scene last time we saw Amazon Lily, when the marines go to take down someone they bring everything they can.
I imagine some marine vessel noticing the Sunny in the horizon, and the first mate asking the captain what to do. "We'll call HQ and try to follow them discretely without getting their attention until the back up arrives. That's goddamn Monkey D. Luffy, son!"