It seems logical that a card would not show as 'in transaction' during the countering process. I assume that the card's status would only change when the trade is accepted. Cards continue to show on our FS/T lists for as long as the offer is waiting to be accepted, and a counteroffer wouldn't change that, it's still just an offer.
Pulling cards physically at the time of the offer makes sense if the offerer wants to be really thorough, or is really confident the offer will be accepted, or wants to photograph them as part of the offer. Otherwise it can be a nuisance; if an offer goes completely ignored (which happens more often than it should), the offerer has to withdraw and refile the offered cards back where they came from. I keep offers in a spreadsheet to help ensure that I don't offer or ask for the same thing twice.