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Not at all. The 1e Beginner box is intended to teach an even simpler version of that edition. other than the very very basics of roleplaying (this is a d20, this is a character sheet, this is a map) the beginner box would not work at all for 2e.
That said the 2e rules are very much simpler and better presented than the 1e core book, and you should be ok learning from the core 2e book. read the chapter 1 introduction chapter, it is very well done for beginners.
What you might want to do is set some limits on your first few games:
For example, limit the players to human, dwarf, and elf heritages, limit the classes to wizard, rogue, cleric (cloistered), and fighter.
That's pretty much how the Beginner Box was structured for PF1. You may want to remove some other rules from your first few games as well: now Attacks of Opportunity for fighters, similar rules limits on the other classes. Again, those simplified rules were a big draw for the Beginner Box.
Play a few scenarios with these basics, while you get comfortable with the ruleset, and then start adding in the rest of the options.
If you're creating a character for society play, you won't be able to adjust the rules, but you certainly can limit your own character choices.
If necessary, play little snippets of a scenario: One fight, one exploration, one downtime at different times, just to slowly walk through each activity. PF2 is quite a lot simpler than PF1 to get started with.
But no, don't use the Beginner Box for an earlier version with very different rules to try to learn this one.