Not normally, but check the installation instructions and fire certification for the door that you're having installed - this should be followed scrupulously. BS 8214 (Timber-based fire door assemblies ? Code of practice) has the following general guidance:
"....9.5.3 Under-door (threshold) gaps for fire resistance
Under-door (threshold) gaps should be in accordance with the fire door manufacturer?s installation instructions for the particular design.
NOTE 1 Gaps larger than those approved are likely to compromise the fire resistance performance of the door assembly.
The door should be able to open freely over its entire opening angle without damaging the seal or catching on the floor.
NOTE 2 Further guidance on threshold gaps is given in the ASDMA publication Guidance and recommendations for the coordination of bespoke doorsets..."