No, in a typical mortgage, anything that becomes a “fixture” or “improvement” even if added by the owner post-mortgage is swept-up in the lien.
To give a more obvious example than an appliance, we put in granite countertops post-purchase. This would be covered by the mortgage.
It only becomes an issue when you use new money from a lender to do improvements, in which case that new lender often has “priority” over the old lender (i.e., gets paid before the old lender).
The definition of what is a “fixture” or “improvement” varies from state-to-state.
In some cases, it does include removable items like refridgerators, washers, and dryers.
In others, pretty much anything that can be unbolted or unwired or unplumbed are not fixtures.
Many people don't realize that the difference between a "first mortgage" and a "second mortgage" is just which was contracted and/or recorded first.
I think your example of a home-improvement loan taking priority over a first mortgage would be extremely rare and would require the permission of the first mortgage holder, evidenced by signing an agreement to subordinate their loan to the new loan.