Scoring of run(s)

[Tru_in_Blu]

I'd like to hear some inputs on this scenario for ASA ruleset:

Two outs, R1 on 3B. B4 grounds out to F6.

A) B4 crosses but does not contact 1B prior to F3 catching the ball and continues far down the RF line. BU correctly rules "safe". R1 scores on the play. The defense becomes aware that B4 missed 1B and now appeals by having F3 step on 1B while holding the ball as B4 walks slowly back to 1B.

The umpire now rules B4 out.

B) F6 overthrows F3 and the ball deflects off the fence down the RF line. B4, seeing the bad throw before getting to 1B, heads to 2B but did not touch 1B on the way by. R1 scores on the play. The defense becomes aware that B4 missed 1B and now appeals by having F3 step on 1B while holding the ball.

The umpire now rules B4 out.

Does the run score?

Thanx.