If I am a member of a group that wasn’t in communion with Rome, and I went to a mass that was being said by a priest that was in communion with rome, then I wouldn’t think that any blessings given by that priest were valid, would I?
I know it’s a weird question but please bear with me as it was an awkward thing to phrase.
If I have correctly intuited what you have written, your question is the opposite of what others are attempting to answer and the heart of the matter is what I have underlined.
In other words, you are asking if – hypothetically – you belonged to a group not in communion with Rome would YOU think that what I did as a priest was valid. The answer is it depends upon the group.
If you were Orthodox or of the Polish National Catholic Church you should see me as being in valid apostolic succession through my ordination. Therefore, my blessings would “work” as those of your own clergy.
Looking toward the Anglicans, the Lutherans and beyond, I would be seen as an ordained minister but their understanding of the nature of ministry is going to begin to move quickly in a different direction from Catholic/Orthodox understanding of the nature of the Sacrament of Sacred Order.
To your specific question, however, and regardless of their concept of a sacrificial priesthood and the nature of the confecting of the other sacraments, they would see my blessing as truly efficacious theologically although the language we would use to theologically explain what happened when I bless would vary.
In communities that have more recently left communion with Rome and are schismatic, however, there will be some who would say that apostolic succession was lost with the post-conciliar rites of ordination – and therefore they would hold that I am not validly ordained since I was ordained following the last council – but those who adhere to that position as a group are relatively few. If you were of their company, you would not see my blessing as valid, to use your expression. Sadly, though, I have met laity who hold that same position but who belong to groups where their clergy, however, do NOT hold that position – thankfully.
The question is assuredly not weird to one who was a professor. Not knowing details concerning the group about which you are theorizing, however, this is about the best answer I can give you in the circumstance.
I hope this helps. God bless you!