Regulators don't limit flow, only the downstream pressure. If the line vents, the vent limiter kicks in and reduces the flow. These are now standard on all new bottle fed gas BBQs.

With a bottle fed BBQ it can be a kind of pain. One MUST open the tank and allow the line pressure to rise before opening a burner valve. Otherwise opening the bottle valve into and open burner will cause the vent limiter to kick in and your burners will work but be choked down. This limits the heat that can be generated by well over 1/2.

A vent limiter is most likely a good thing, especially if any of your connection to the house is exposed.

My preference would be to connect the hard outlet to a valve, followed by the vent limiting regulator, followed by the adapter line leading to the BBQ.

Edit: It seems I may have misunderstood the term "vent limiter"

Here is the relevant weber grill faq.