I am thinking of installing a Natural Gas Williams Monterey Top-Vent Wall Furnace, with 35,000 BTU
In my finished basement. I have three heat registers but the temperature in the basement isn't as warm as we would like especially when its below freezing out.
My question is, since the wall unit requires a vent source, can I tap into my main units vent? Is there a code I need to abide by and what do you think the cost would be to have a HVAC tech do the work? Thank You.

You need to follow the manufactures install instructions to the letter. If it does not show the setup you want to do then do not do it. Most of those units like you have use specific venting directions and I have never seen one that would allow a common vent like you are talking about doing. CO poisoning can be a major problem when you vary from the factory directions.