Yes. Just like you said, it is no longer $1200 on a $4800 limit; it is now $1200 on a $0 limit, hence it is maxed out (by a lot) and therefore affecting utilization and dragging your scores down.
Synchrony appears to report the original limit on the closed account. 
My experience has been no, my BB&T closed with a 4055 balance of a 4500 SL and that the SL is what reports each month.
@Anonymous wrote:Nothing negative, no lates...
Sync closed all my accounts as I mentioned in other post.
How does that affect me with respect to the $5,500 I owe on closed accounts?
Does it hurt me to owe $1,200 out of what was a $4,800 limit because now it must show closed with balance of $1,200 on a $0 limit card.
MyFico has not sent me alerts I found out when my Amazon purchase of $38 was denied.
Some lenders will leave the limit where it was, in terms of reporting, some put in a lower limit. So it's definitely safer to get rid of them if you can.
@Anonymous wrote:It will only hurt if Synchrony reports the closed card with a $0 limit. If they continue to report the original limit, your utilization will stay the same until you pay it off.
Actually the utilization would not stay the same, because the card's limit has been removed from available credit limits.
@Remedios wrote:@Anonymous it wont hurt
It's a myth that refuses to die.
Most accounts that were closed (without being charged off) will report limit and balance.
In fact, some people will close cards when lender announces future changes (such as APR increase) to preserve terms.
Even when the lender does report the correct limit, it still hurts, because the balance is still there in the numerator, but the credit limit has now disappeared from the denominator, in computing aggregate utilization percentage.