Order of adding chemicals - is the only reason to add chlorine before the stabilizer the concern of having to use more chlorine if you are having a possible problem?

If someone added stabilizer and then a little later the ph down but didn't realize that they should have added the chlorine first, can they go ahead and add the chlorine after that - since the pool needs chlorine?

Appreciate any thoughts on this so I can go put chlorine in the pool...

Thanks
Renee