Latency: separate input and soundcard?

In order to reduce latency, does it make sense to monitor from the soundcard separately?
 
I'm running Sonar X2 on an old Core Duo laptop. Using a Lexicon Omega for I/O, and I'm getting about a 20ms round-trip latency. Trying to play lead guitar of do anything remotely timing sensitive is problematic. Using ASIO, and have the latency slider down to the next-to-the-last setting (last one produces unstable audio).
 
There is a sound card built into the laptop. Not happy with the cabling options (no way to do headphones and attached monitor speakers without an outboard switch).
 
So the question is, during recording situations, would the apparent latency be decreased if I used the built-in sound card for output instead of routing back out the USB to the Lexicon? 

Although the onboard audio chipset is connected physically to the motherboard, it is connected logically via a driver that is almost always much slower than ASIO.  As Larry says you can get to effectively zero latency with your interface if timing is the problem--the signal you hear never enters the computer but just loops back electronically as an analog signal to your output speakers or headphones.
 
Incidentally twenty milliseconds is much faster than your brain can receive and process the sound and then send motor impulses to your hands. That physiologically limited reaction time is longer than 200 msec. Musicians do not coordinate their playing by mentally processing each note and adjusting the next note on the basis of the last note they heard. That is physiologically impossible. They adjust the speed to an internal brain metronome commonly called finding a groove. Some people can tolerate a pretty long latency in the feedback from what they have just played without getting lost, and that can improve with experience. 

Thanks to you both for quality feedback.
 
The drive says 20ms, but it sounds longer. 
 
That being said, I picked up a Digittech RP355 on the cheap this weekend, and I'll see if I can split the signal, getting some effects outside of the recording input chain and clean signal going in (wich me luck).

Thanks. Interesting, but it had no effect on perceived latency on my humble little studio. Since the integrated sound card and the Lexicon are the only sources, I'm still stuck.

Investigating signal splitting now ... seems like the only good option.