Yes, that can happen
There are 2 wires on ignition switch under steering column, one powers coil/spark in RUN, and the other powers coil/spark in START
Seen in this diagram:
https://www.therangerstation.com/tech_library/EDiagrams/files/Diagrams_StartIgnition83to88_2_3.JPG
The red/green stripe wire has 12v in RUN, but no 12v in START, the Brown/pink wire has no 12v in RUN but has 12v in START
This is from the old days when a Ballast Resistor was used in RUN, to lower voltage to the coil, but needed to be by-passed in START for stronger spark on cold starts
Ignition switches still had this for a few years and some still do , some systems like radio power is cut off in START
Use a test light or volt meter to see if you have 12v at the coil with Key on(RUN), you already know you have it in START
Then move to ignition switch to test red/green wire