To make this clear, this falls completely out of the realm of officiating. This is not a rule in a sports rules book, it is solely handled at the school administration and VHSL level. But, I do own a copy of the VHSL handbook so here's your answer.
"PM 27-11-6 (1) SPORTSMANSHIP RULE/Player and/or Coach Ejection Penalty (4-00)- Players and coaches who are ejected from a contest for unsportsmanlike conduct and are ineligible for the team’s next contest(s) . . . must sit out the next contest(s) played by the same team, meaning that if the ejection is from a varsity contest, the penalty is applied to the next varsity contest(s); a junior varsity ejection means the penalty is applied to the next junior varsity contest(s). Further, the penalty means a LOSS of one or two contests under the Contest Limitation Rule, and a player could not suit up for games at another level of competition to replace those he/she is required to sit out."
So to answer your question, yes the player can play a varsity game the same week he is suspended in JV, but the suspension counts towards their Contest Limitation, meaning they lose 1, 2, etc. games of eligibility that season. So, if they play varsity the week they're suspended in JV, they're losing potential playing time at the end of the year.
Again, officials will not get involved in these issues on the field. It will be handled outside the confines of the game by the administrators.