You can actually achieve a dynamic background by starting with your type-on-path circle with the text and ensuring the path options have your text aligned by the "Ascender", which will make the text be contained inside its path shape.
At this point you add a new stroke below the characters and apply the Convert To Shape effect as an Ellipse, with the proper relative negative width/height settings to tuck the new stroke below the text as needed.
Then you add a new fill also below the characters and this time do an Offset path on it so it forms a blob behind the text. Enter such an offset setting that will make this background blob engulf all of the letters and then some.
This is where either you'd need to add | pipes | to the text or otherwise be ok with potentially a jagged or different-sloped edge where you wish to have a straight edge. However there could be more ways to deal with this using even more effects - but for now, let's accept the jagged edge.
So once the fill is in place, you may just be ok with the white-on-white background which will produce a similar visual result as your background blob will be the same color as your background - or you may want to turn the opacity of the new fill to 0% and enable Knockout Group option in the whole object's opacity settings. This will knock out any transparent background.