We will be in Florence on the first Sunday in November and know that the Uffizi has free admission. Thus we expect long lines. Can we skip the line if we purchase a Firenze card? We are only in town for the one day from a cruise ship.
I've seen multiple mentions that waiting line (not security check) skipping is indeed possible with the card on free Sundays but it never hurts to double check JUST in case there has been a recent change. You might inquire at this address on the Firenze Card website?
While priority access may be possible, the most popular of museums free on this day will be mobbed. When they are filled to capacity, everyone must wait until enough visitors leave before more can be admitted. It's not a day I'd personally choose to do either the Uffizi or Accademia if there's an alternative but I understand your predicament. It may also not be quite as swamped in November as in summer/shoulder season but I won't swear to it.
I have 2 family cards valid for one year costing 140 euros for both. It is valid both for Pitti Boboli and Uffizi. For non family persons it is 100 each.
When I go I never have long queues, however there is a security check ( bags, coats etc are checked) and it does take some time. Before that even though I have free access with these cards, I need to get a free entrance ticket. I believe you will have to go through a similar procedure.
Try to go early in the morning.
In my one experience of this on a 'heritage day' when the museums were free my pass did nothing. I had to line up with everyone else at Palazzo Pitti. Since the Uffizi actually has a separate door for pass holders it is worth a shot to see if you can use that.
These are two websites with mentions about the card and free Sundays:
http://www.uffizi.org/1588-revolutionary-changes-in-state-museums-starting-july-1st/#comment-3360
https://www.visitflorence.com/florence-museums/is-firenze-card-worth-it.html
But I would write them via the address posted previously.