It can. Heavy eye strain, especially when your eyes are struggling to focus or you're battling glare and a poorly positioned screen, can leave some people feeling lightheaded or slightly queasy, often alongside a headache. It's usually mild and eases once you rest your eyes.
Relieve it the usual way: take breaks (the 20-20-20 rule), match brightness, cut glare, fix your screen distance, and hydrate. If dizziness or nausea is frequent, severe, or happens off-screen too, that's worth seeing a doctor about, it's beyond ordinary eye strain.