Nope. Sirius A is spectral class A0 - white or bluish white. The companion is far too faint and close to it to see naked-eye - a ten-thousandth as bright.
The description of Sirius as "red" very likely is because it looks red when it's just rising over the horizon, just like the Sun does. The first pre-dawn rising of Sirius was what told the Egyptians that the Nile was about to flood - the most important astronomical event of their year. It was red at the important moment, but once it was up in a dark sky it was the same color 3000 years ago as now.