From what I've seen, in my view, the answer is a simple yes.

As for studies, there is an article in Psychology Today which cites a particular study called 'Interspecies Parenting: How Pet Parents Construct Their Roles'.

Links to both below:

https://www.psychologytoday.com/us/blog/head-games/201903/why-some-people-think-pets-children-and-others-dont

https://www.researchgate.net/publication/322261554_Interspecies_Parenting_How_Pet_Parents_Construct_Their_Roles