Can Tamilians understand Telugu?

 Yes. Most of Tamilians understand Telu(n)gu because over one fourth of Population in present geographic boundaries of TN have Telugu Ancestry.

The other reason is that Telugu spoken in TN, except bordering districts, is atleast 800 years old and has influence of Tamil words in it. Only 5–6 percent of TN people in bordering districts, can read and write in Telugu.