$600/week/person over any reasonable period is hardly enough to trigger serious inflation worries in the short or medium term. Even if you apply that to everyone in the US, you're looking at $180 billion a week, against a GDP of $20.54 trillion.
If you compare the stimulus payments in similar annualized terms it is nearly half of GDP. $9.36 Trillion.
Having said that, the relevance of GDP in a conversation about inflation is unclear to me when GDP does not account for inflation.