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.researchgate.net/publication/322261554_Interspecies_Parenting_How_Pet_Parents_Construct_Their_Roles which can also be viewed at https://doi.org/10.1177/0160597617748166
