That shouldnt happen.
Leyline nexuses in the Dresdenverse dont work the same way as in WoD; here, they are confluences.
You should be able to drain whatever the potentia/tass is that is required for making Wonders, but you cant deplete the Dragons Nest magic itself, any more than you could drain the ocean. Not how Dresdenverse magic appears to work.
I'd go digging for canon references, but Im sleepy right now.
You're talking about the equivalent of sticking a straw in the ocean.
Power isnt as dense as it used to be in the Age of Legends, but there's still a fuckton of it floating around, and a Dragons Nest is seeing a shitton flow in and out per second from the leylines that cross over it
You would have to drain every leyline running in and out of this confluence to have any sort of effect on the magic level in this spot.
And too many leylines are apparently connected for that to be feasible.
Or not have major effects on the local magical ecology.