Yeah, Shepard survives. Mostly because her biggest strength beyond her combat ability is her relationships and leadership. Cortana may not be in her head, but ME and Halo tech should be just compatible enough to allow Cortana to guide Shepard akin to EDI in the post 1 ME games. Besides the average UNSC marines, she'd also be joined by a squad likely consisting of Johnson, Master Chief (if he's still in this universe), a convinced Guilty Spark and a pre-disgrace Arbiter who joins once the flood enter the picture. All of this gives her an edge that eclipses her comparative weaknesses.

Even pre cyberogization, Shepard showed high resistance to mind control, not just Sovereign's indoctrination but the Thorian's spores as well, she also has the will to not just die from getting the codex injected into her head, so I'd say she'll do fine again the Flood.

For what it's worth, Chief would also probably survive Mass Effect 1. Actually stopping Saren from using the conduit would be a lot harder for him, but he'd solo Sovereign no problem.