Yes, you can do this, but you will need to do some manual editing within the view .xsl files.

When you insert something like a layout table, it automatically uses the themed classes, but when you select a theme color from the color pallett, for some reason, InfoPath inserts a hard-coded physical color (i.e. "BACKGROUND-COLOR: #517dbf") instead of using the theme class (i.e. class="primaryDark")

In order to make your view fully theme changable, you will need to manually edit your view .xsl files to find all occurances of a hard-coded theme color, and replace it with the corresponding theme class. If you are familiar with HTML, then this should make sense.

Once you've made this conversion, then when you switch themes, in InfoPath, all of the colors will be updated as you expect them to be.

I hope someone can help me!

Can I design my own template, no matter how complex it is, and be able to
change its colors by selecting different color scheme? I tried everything. I
just could not persuade my template to think of colors as they are from color
schemes. Just do not tell me I have to start all over again!