The Aviva Premiership club were summoned over their fielding of an ineligible player - scrum-half Tyson Keats - in what is understood to have been nine league games this season.
But the RFU have announced that a decision has been deferred.
"The panel of Jeremy Summers (chairman), Mark McCafferty and Peter Budge will now consider their decision, which will be communicated in due course," the RFU said in a statement.
If the case goes against them, then Welsh could find themselves hit by a points deduction that could effectively decide their Premiership fate.
Welsh, who were promoted to the Premiership last summer, are currently engaged in a fight to avoid relegation with Sale Sharks and London Irish.
They are three points above bottom club Sale and two behind 10th-placed Irish with five league games left.