Yes, you can!

In addition to filtering the sales channels at the product level, filtering at the variant level is supported as well.

When configuring the Data Settings, simply add a filter like this under the Custom Filters section:

•     Variant Publications Channel Names contains Point of Sale

You can add multiple filters for different combinations of sales channels.

One thing to note with variant-level sales channel publishing, however, is they don't automatically get unpublished when the parent product is is unpublished.  The API will still show the variants published to the sales channel unless you explicity unpublish them at the variant level as well.

Since the variant is technically not published if the parent product is unpublished, it's a good idea to filter both at the product level and variant level in this case.

For example:

Data must match: all conditions

• Product Publications Channel Names contains Point of Sale
• Variant Publications Channel Names contains Point of Sale

This way, if the parent product is unpublished from the "Point of Sale" channel, all variants of that product are also automatically filtered out.