As long as you have split tunnelling enabled, then if you don't send down a DNS entry as part of the VPN negotiation the PC will continue to use the DNS entries it received upon bootup, which is normally the ISP's DNS servers. With split tunneling enabled, you will be able to do DNS queries "in the clear" to the ISP DNS server.
Keep in mind that if the slow response they're reporting is for everything (ie, web pages are slow to download), it may not be a DNS issue. DNS issues normally look like very slow response initially (while the PC is waiting for the DNS reply), but then once a page starts to load it loads quite quickly, and that same page continues to load quickly because the DNS entry is then cached.