Yes, that’s right. If you toss the keycard at that point you are stuck and need to reload. But anyone who throws a keycard away amidst such dangers must be tired of living anyway!
If you used the syringe on Suave Blanc and successfully answered his questions, he will give you the L3 keycard. If you fail the questions, he will slump back into his state and you will be unable to proceed, requiring a reload before the failed questioning.