clear answer: purely on Linux itself:
NO. But if you share NTFS partitions between Linux and Windows, or if you use USB flash keys, then, yes
Because you could always without being aware of anything get malware on Linux, that won't harm linux, but will leak into Windows. This said, even if it's not the case currently, I've been dual-booting Windows with Linux a long time, and installed avast for Linux just once, and kept it very shortly, ie I just took the risk with no AV on Linux and nothing ever happened...but I don't share NTFS partitions (NTFS-3G disabled), and I scan my USB keys when I'm back in Windows.
This all also depends on your browsing behavior.