Yes. The world is governed because it belongs to the Divine goodness, as it brought things into existence, so to lead them to their end, and this is to govern.
Mundus gubernatur quia ad divinam bonitatem pertinet ut, sicut produxit res in esse, ita etiam eas ad finem perducat, quod est gubernare.
In all created things there is a stable element, at least primary matter; and something belonging to movement, if under movement we include operation. And things need governing as to both: because even that which is stable, since it is created from nothing, would return to nothingness were it not sustained by a governing hand, as will be explained later (Q104, A1).
In omnibus rebus creatis est aliquid stabile, ad minus prima materia; et aliquid ad motum pertinens, ut sub motu etiam operationem comprehendamus. Et quantum ad utrumque, res indiget gubernatione, quia hoc ipsum quod in rebus est stabile, in nihilum decideret (quia ex nihilo est), nisi manu gubernatoris servaretur, ut infra patebit.
The natural necessity inherent in those beings which are determined to a particular thing, is a kind of impression from God, directing them to their end; as the necessity whereby an arrow is moved so as to fly towards a certain point is an impression from the archer, and not from the arrow. But there is a difference, inasmuch as that which creatures receive from God is their nature, while that which natural things receive from man in addition to their nature is somewhat violent. Wherefore, as the violent necessity in the movement of the arrow shows the action of the archer, so the natural necessity of things shows the government of Divine Providence.
Necessitas naturalis inhaerens rebus quae determinantur ad unum, est impressio quaedam Dei dirigentis ad finem, sicut necessitas qua sagitta agitur ut ad certum signum tendat, est impressio sagittantis, et non sagittae. Sed in hoc differt, quia id quod creaturae a Deo recipiunt, est earum natura; quod autem ab homine rebus naturalibus imprimitur praeter earum naturam, ad violentiam pertinet. Unde sicut necessitas violentiae in motu sagittae demonstrat sagittantis directionem; ita necessitas naturalis creaturarum demonstrat divinae providentiae gubernationem.