It will, but pretty much every local taxi company will be familiar with airport runs - it's great business for them, after all. It's not hard to pre-empt the traffic, check flight arrivals (particularly in these days of smartphones) and park up somewhere near the airport to await the phonecall from baggage claim.

(If you use one regularly, they'll also often ask if they can pick you up somewhere outside the chargeable area, if applicable, at a discount to both of you...)

This is my experience, anyway.

However, I still think the OP's blood pressure will be high along the M4 if their meeting is really "only a couple of hours" after landing...