Yes it is.外堀を埋める literally means to fill up the outer moat (which makes it easier for an army to siege a castle or fort.) The expression means to get rid of obstacles on the way of what one wants to do.
It means smoothly or swimmingly or without a hitch. His whole sentence means. Because all obstacles had already been eliminated without ティアーヌ noticing, he/she ended up having to marry without a hitch.