As Spotter says, area controllers often filter 7000 squawks out since they're almost all at low level, hence of no interest to their airways traffic. Approach controllers, however, will often be keeping an eye on 7000 codes since they often call us up asking for a FIS or zone entry, the little monkeys! (only kidding!). In order to identify you, and if you've got a transponder, you'd be issued a discrete squawk. Depending on the speed of the secondary radar head, it can take a few seconds for the display to update, hence the delay you referred to.
Also bear in mind that a 7000 squawk on a VFR aircraft is about as vague as you can get - it just says to the radar and TCAS receivers "A plane's here". In order to positively identify you, or provide any service other than FIS, or to check your Mode C, I'd definitely be wanting to identify you with one of my own squawks, and watch it appear as I peer into the screen....be cautious of people giving you information based on an assumed ident!
Final point....at my (northern) airport we only filter out upper airway level stuff, hence we see everything at lower levels - I'd say Mode C is extremely useful, since even though you might be passing our zone without speaking to us, and hence we can't verify the accuracy of your Mode C, it still gives us a rough idea for traffic information / avoiding action purposes.
Hope this makes sense!
PS Don't use code 7001, cos in the UK, it's allocated to something - and it's not you and your Cessna!!!