Can I feed a 5V boost converter with 4xNiMH cells?
The issue is quite simple:

Consider a boost architecture:



If Vin is above the programmed Vout, then D1 will forward bias, feeding Vin to Vout. The loop will attempt to compensate by reducing output drive, but it will be powerless and you will simply dump Vin (minus a diode drop) across the load.

What will happen to loop stablity or the controller is device dependent.

So the answer is - No, keep Vin below Vout.

[Update]

I would be far more concerned about loop stability than the small amount of time that Vin would be above Vout.