Can MCP16251/2 DC-DC step-up converter tolerate higher input voltage than the set output voltage?
The device data sheet says this on the front page: -
• Maximum Input Voltage ≤ VOUT &lt; 5.5V

So, you have to be careful.
But the device data sheet also says this (note 2, bottom of page 3): -
For VIN &gt; VOUT, VOUT will not remain in regulation.

I take this is a favourable indication that if you can live with the output voltage rising a little above the natural regulated voltage on fresh batteries, you will be OK with this device.
However, there will be side issues because when the battery voltage exceeds Vout, the synchronous MOSFET inside the chip will switch off and then you will have one diode drop between input voltage and output AND, this is likely to cause the synch MOSFET to turn on and route full input voltage to the output.
The problem here (although it may not manifest itself as a real operational problem) is that the output voltage might oscillate between 3.3 volts (the regulated desired output voltage) and the fresh battery terminal voltage. That might mean your output voltage is a DC level of (say) 3.35 volts but changing from 3.3 volts to 3.4 volts at several kHz.
If you can live with this then that's OK but, it may behave itself - difficult to tell.