Yes, if the tie points of the second image are only concentrated in a small area, that will affect the ortho accuracy of the second image. Think of it as fitting a line y = x with only a few points that are close to the origin. The slope won't be well constrained and the same will happen with your images. If you have small geometrical artifacts or some noise on your GCP, it may be a bit amplified away from the GCP. But of course it all depends on what "small overlap means". Give it a try anyway. If you're careful in choosing tie-points and if you have some nice features to provide accurate correlation, it might work well enough.
Using the shaded DEM as the first image is never very accurate but it's good to make sure that your ortho-images are well registered to the topography. It's important if you have strong topo features in your images. If the image and your DEM aren't well co-registered, you'll be correcting for topo features that are not well located in the images and will introduce topo residuals. If you think your other sources (Landsat or ASTER 1B) are well registered to the topo model you'll be using to create your ortho-ASTER, using them as reference should work. But remember that 1B images are only projected on an ellipsoid and aren't rectified for topography. Therefore, to avoid being too inaccurate, select only tie-points on areas with smooth or flat topography. However, it might just be better not to use any tie-points than using a bad first reference image. That all depends on the accuracy of the ancillary data in your ASTER L1A. As a test, orthorectify your ASTER image without any tie-points or GCP (still use a DEM in the ortho-generation), and try to assess how far the topo-features in this ortho-image are from the features in the shaded DEM. If they're close, maybe you don't really need GCPs for your first image. You can also try to orthorectify both images without any GCP, and see what the registration looks like. Usually the tie-points are necessary between the second and the first image, but the tie-points on the first image can sometimes be neglected, it depends on the accuracy of the L1A metadata in your image, which can vary.