Is it possible to somehow make an application's setting (I mean a checkbox-type setting from "Settings -> Configure ...") into a toolbar button (without programming)?

Unfortunately, this is likely not possible as toolbar checkboxes require specific programming from what I recall.
XMLGUI only has limited support for checkboxes, and additional code is necessary to monitor the change and propagate the setting unfortunately.

bcooksley wrote:Unfortunately, this is likely not possible as toolbar checkboxes require specific programming from what I recall.

I meant that the setting as checkbox could be very well just a button on toolbar - whether it's on or off.

Which application and setting is this?
Some applications do offer the option to set certain settings via menu entries and the like, which may allow this to be setup.

As a general rule however, this is not possible (even if using push buttons as you mention above) due to the need for extra code to propagate the settings.

I'm interested in KMail2's setting "Reply using HTML if present". I guess I should then add a feature request for getting this button to toolbar

In this instance, I would definitely recommend a feature request.