When you apply to a job posting, your name and face are shown to the client.
If he is paying attention, then yes, he could figure this out.
Or he might just remember you.
If a client hires a lot of freelancers, he might not pay attention that much and he may well not remember you.
Hi Sarah, it depends on how you performed in your previous project of the client, for now, Upwork doesn't show any special notification about you to show that you have worked for him before.