Honestly, I'd have to review the 5Y3 data sheet to say, which I'm feeling too lazy to do at the moment. So long as the peak current draw doesn't exceed the the capablity of the 5Y3, you're probably safe.
The peak draw will occur when the caps. are completely discharged, which typically means at the moment of power switch-on. However, the 5Y3 will need to warm up, and so will progressively conduct as it warms up, not conduct immediately the way a silicon rectifier would. Which means the worst case peak current draw at power-on will be reduced.
