Replacing processors in a notebook is difficult anyway, and you need to make sure that:
1.) The Celeron M uses the same socket as the Pentium 4
Nope. The Celeron M is a Socket 479 (original) whereas the Pentium 4 is 478. The sockets are pretty close if not identical physically but the pinouts are different.
2.) The chipset supports the Pentium 4
The P4 uses an 845 or 855 chipset while the Celeron M uses the 855 or 915 chipset.
3.) Both processors have a similar TDP.
That will be not be true. The Celeron M has a TDP of under 30 watts while the P4 2.6 is at best 35 watts (P4-M 2.6) or much higher if it is the desktop version like many P4 desktops back in that day were.
Anyway, even if it did work, the P4 2.6 wouldn't be very much faster than the Celeron M 1.6.