Everyone goes through screening, regardless of what they are doing with luggage. You need to get that barcode on your passport which shows you've been screened.

When I last travelled from TLV in Club I was directed to a shorter queue at the 'triage' point at the start of larger snaking queue. I'm not sure if this is a consistent policy and signage is very ambiguous at that BA end [area A?] of T2. As I travelled in WTP last month I wasn't able to determine if there was a different queue. In any event, the main queue moved quicker than I thought. And if you are running late I saw people negotiating with the helpful airport staff at triage point to go speed through. Which was a surprise for perceived TLV gruffness!