Lightning QuickAction (API) without modal
I asked in the Lightning Trailblazers org62 group about this, a few months ago, and the response we got was that SFDC understands this usecase but do not have an estimate for delivery yet.
FWIW, we created a custom component with a button that sits on the lightning page, instead of using a quick action. Initially we displayed a spinner inside the quick action modal, so it wasn't completely weird.
Just add the below code in your component so that it doesn't show up the modal when you click on the Quick action button
<aura:html tag="style">
.slds-backdrop {
background: rgba(43, 40, 38, 0) !important;
}
.slds-fade-in-open {
display:none !important;
}
</aura:html>