Not at all, the earth zips around the sun at a pretty fast clip, approximately 18.5 miles per second, so at any time electromagnetic radiation from the distant stars approaching the earth would be Dopplered by that amount, corrected for the direction it was coming from. A star you observe directly in front of the earth would have a blue shift due to that speed. If the star was located at right angles to the velocity vector of the earth the radio waves would be hitting us at a right angle to the direction of travel at that moment so there would be no Doppler shift. This effect varies with the direction the star appears to us, and the vector itself is constantly changing direction as the earth travels in its orbit.

You have to correct for both the angular distance of the star above or below the ecliptic plane (pitch) as well as the angular distance from the earth velocity vector in the ecliptic plane (yaw). The earth's velocity vector does change direction, about a degree per day, but that should not make much difference over the few minutes it takes you to take an observation. But the correction would be very different for observations of the same star taken months apart.

A similar effect is at work due to the earth's rotation on its axis. The planet spins about a 1000 MPH at the equator (much slower!), and this velocity decreases as you go north or south. At the poles it is zero. But the velocity vector of the receiver changes direction about 15 degrees per hour, and again the position of the star must be corrected for. A star at the pole would have no Doppler correction, it doesn't appear to be moving to your antenna. A star on your meridian would appear to be moving at right angles to the antenna so it would not exhibit any Doppler shift either. Anywhere else, the star would require a correction for frequency, which apparently you already exploit as you mention in your earlier posts.

So to Doppler-correct for earth's revolution AND rotation, you need to know the RA and Dec of the star, the time of day, the position of the earth in its orbit, your latitude and longitude, and the obliquity of the ecliptic and do a lot of trigonometry to calculate the summed velocity vector due to all these motions. This would have to be done automatically, the only numbers you know ahead of time are the star's celestial coordinates and your antenna's terrestial coordinates, and the obliquity. The position of the earth in its orbit would have to come from an ephemeris, and a clock would provide GMT.

I haven't actually carried out these calculations, but I suspect that over the short length of time you are integrating an observation (a few minutes), the numbers would change very little, but if you observed the same star over a period of hours, it might make a big difference. Apparently, your equipment is capable of detecting the minor frequency shifts caused by rotation because you mention you utilize them to verify the cosmic origin of your source (a geostationary satellite is motionless to you). But this rotational Doppler is much less than the revolutionary Doppler.

To complicate matters, the earth's orbit is not circular, and its speed varies, so if you need super high precision, a lot of number crunching has to be going on in the background and your receiver must constantly be re-tuning to correct for this Doppler shifting. This need not be done during the observation, perhaps you could do post-processing of the data.

I don't know enough about radio engineering to know if this is even a problem you have to worry about, these velocities are very slow compared to the speed of light. But if your equipment is capable of detecting these minute Doppler shifts, and if they can push the signal outside your bandwidth, then you'll have to correct for them.