It can, yes. So can a funky kill switch.

WELL IT GETS SPARK WHEN ITS COLD BUT AFTER I USE IT AWHILE & THEN TRY TO START IT AGAIN IT HAS NO SPARK.

First replace the coil. If that doesn't work then replace the kill switch.

90 % of these failures are coil related when the complaint is as described. Very rarely is the ignition on/off switch the culprit , but this can easily be tested or bypassed (jumpered) to verifiy when it occurs once the unit is hot .
Older models with points and condenser displayed this tendency frequently back in the day .