Yes Rusty it does, infact all security programs interfear with internet speed.
The easiest way to tell is to disable all security for your PC then do a speedtest and save the results.
Then do the opposite and see the difference.
Its also worth remembering that your DHCP device or more commonly known as your Router as with all they have built in security features to.
Everything that comes down those wires is inspected as packets of data.
Imagine the ethernet cable has 65000 wires for data to pass along.
Now your DHCP/Router will inspect the packets of data there are 65000 ports for the said data to pass through.
However the data will get held up for inspection at the ports (think of the wire to be simular to a 65000 lane motorway and the 65000 ports like toll gates) so without the correct toll the port will not open, so now the data jumps to the next port and so and so on.
Granted all of that happens in milliseconds of time but those milliseconds make seconds and seconds make minutes and minutes make hours gettin the picture.
Also it may be worth changing DNS servers in your router configuration.
In simple terms the DNS server is like a giant telephone directory and there we have access to 2/3.
Your ISP will automatically asign default ones which aren't always the best.
What the DNS server does is break down
www.whatever.com into what numbers it needs to find said address as computers comunicate in binnary code, so if your request goes out and can't be found in the DNS list in your cache on your pc then it goes out to primary DNS then secondary DNS then finally the public DNS.
Have I lost you yet.
I'll stop runing on now so in answer to yor question YES all anti spyware programs will slow down internet speeds, its there for your protection as it handles and inspects packets of data coming into your pc for threats.