Not quite clear on which one you plan to substitude for which, so here is the answer either way:
Yes, you can use a DS18B20 to replace a DS18B20-PAR without problems, just connect Pin 3 (Vdd) to your power supply.
No, you can not use a DS18B20-PAR to replace a DS18B20 unless you modify the circuit. The reason is that the PAR version requires a "strong pullup" during temp conversion. Page 3 "Parasite Power", and figure 2, of the DS18B20-PAR data sheet has the details. If the number of PAR units is small, you can (I have) eliminate the MOSFET they suggest and just hook it directly to a pin to drive it, as the total current is well below the 25ma limit of a single PIC pin.
HTH,
SteveB
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