It is correct, but it definitely seems awkward.
With an "if/then" statement like we have, we use a "time-shift" subjunctive in the "if" clause and a conditional verb in the "then" clause:
If I were king, lawyers would be outlawed.
To form a time-shift subjunctive, we have to figure out which tense the verb would normally be in, then step back one tense. When the verb would normally be present tense, we step back to simple past tense (as in the king/lawyers example) When the verb would normally be simple past tense, then the subjunctive becomes past perfect: If I had been there, the game would have had a different outcome.
In this case, we're talking about an event "tomorrow", so we would normally use present tense (since we must be talking today for tomorrow to make sense). For time-shift, we use past tense: if Sophie ate pizza tomorrow. We then use the conditional "would" in the consequence clause: she would become ill.
