most malware can run using only a few kilobytes or megabytes of ram and some do not even have a listed process within any standard program (as in you have to go to special, devoted thirdparties for their programs to see what is really happening)
I've had avast and other AV's block malware just from banner ads and silent drive-by attacks on SAFE websites
only the bad malware code tends to get noticed unless the goal of the malware IS TO BE NOTICED, ransomware for example.
it is not as easy to get infected just by connecting to the internet now, but it still happens!
if you want an antivirus that is minimally intrusive, does not write to the hard disk for signatures, can be installed to an external drive if desired and uses a MINIMAL amount of system resources, try Panda antivirus. It's free and developed in Spain. Only issue now and again is a false positive, but it's rare