No...why take the risk.
I would maybe put it on for a min for a wrist show but that's it.
I have measured wrist watches with crazy levels of radiation but like its been said its all about exposure over some period of time. And in most cases you have to be with in inches of the dial side to get the full brunt of it. The case back side level are significantly less based on what I have measured.
Example Enicar Seapearl 600....150uSV/hr dial side with in an inch; <10uSV case back side with in an inch.
My watch radiation test:
https://www.youtube.com/watch?v=bAcApQYsATA
Sensor used for measurement was an LND7317...which is very sensitive to alpha, beta and gamma radiation.
If your going to dabble in watches with Radium lume get a good geiger counter so you know what you and others may get exposed to. In the end you not the only one getting exposed. Keep that stuff away from kits and pregnant women and your pocket:)