It depends on what you're on. You need to look up how long a specific medication will stay in your urine.
For instance, Val will stay in your urine for 3 weeks so to be safe you want to be a month sober.
All in all, if it stays in your urine for more than 3 weeks this method isn't worth it seeing you've already taken the meds, you'd have to stop taking them for nearly a month to get it out of your urine, and the fact you ordered specific things shows you need it so going off it right away just for a urine test might not be ideal.
I believe, now I'm not 100% sure about this but one thing they can notice is the urine's date. Once you hand it to them, don't you think they'd find it suspicious that it's moderately cold assuming it began it's defrosting before the visit? I'm not sure about this, but I'd suggest looking into another method to potentially mask it or have a background story ready on hand on why it's in your urine.
Best wishes,
-VII