No they won't. As they're free versions you have to run manual scans so no two run at the same time, otherwise they'll take too much resources of your machine.
May I suggest another two you should consider to have.
SpywareBlaster;
http://www.javacoolsoftware.com/spywareblaster.html . This is a free program and 'blocks' malware before it can install. It doesn't 'run' as such but acts a bit like a firewall if you like but isn't a firewall. You'll have to remember to update manually with the free version.
The other one is CWshredder. I'ts been discontinued for updates but takes care of browser hijacks. Very handy to have as some of the older malware sometimes rear their ugly heads. Link:
http://www.intermute.com/spysubtract..._download.html .