No. You are not carrying it out to the next logical step in the rules for ability check adjudication. When the DM sets a DC for an attempt to intimidate, they also set the success and failure stakes. That is when the DM decides how the NPC reacts. They act one way when there is a success on the ability check, and they act another way when there is a failure on the check.
and none of those need be what the PC wants as an end result.
A PC fighter comes across a lone orc guarding a pie.
"I intimidate the orc" the player says, but adds some flavor to suit your game in how he will... and then tell you he wants the orc to runaway scared
The DM already knows the orc will most likely not run, but sets a DC to see if he successes in intimidating him... if succeeds the orc punches him, if fail orc laughs at him
The PC declarer intent.
the DM determined that the effect was out of line but other effect would trigger off success/fail
DC set
roll made
outcome resolved...
now by my house rules if the PC missed by 2-3pts he would "ha, good try, no" if he missed it by more then that but less then 10 he would laugh a belly laugh. if he rolled more then ten laugh he would laugh hard at him...
if he made it by 5ish I would just have orc punch character in face if he made it by more then five i would have him attack with disadvantage, and I would RP him being freaked out.
as you see my house rule is separate from the main rule
Now the DM at any point could just say "no" or "Ok" for auto sucess/fail thats fine... the roll is if the DM doesn't know.
now reverse it. the orc wants to intimidate the PC into running instead
The DM declarer intent.
the PC determined that the effect was out of line but other effect would trigger off success/fail
DC set
roll made
outcome resolved...
now my house rule part is it doesn't have to be this rigid, the Player (or DM) doesn't need to decide before roll what all the out comes are, they can make them up as they roll before they roll or after they roll.