Replacing a NTC in Meanwell Power Supply
If the NTC is near the input terminals/connector than it is almost certain that its function is limiting the in-rush current at power-up.
IEC 60950 and UL 60950 clearly states that almost all PSUs must limit the in-rush current at power-up.
If an NTC blows a few seconds after power-up than the problem might be more serious I think.

To answer your questions:

No, I don't think the PSU will &quot;feel&quot; the difference.

The start-up will be slower and the 15 Ohm NTC might get hot under full-load conditions.