That would be around 1 nCi (37 Bq) of Po-210, which would be very detectable.
Bioassay (urinalysis) for Po-210 can “see” ~0.05 pCi/liter (1e-17 g/liter) – could get a wee bit lower level of detection with a longer count time.
That is the great thing about radioactive material – you can detect very small quantities of it using relatively simple equipment. It is also what makes it scary to people – because “if you can measure it, then it must be dangerous”.
