The only risk here is if your previous chain was sufficiently worn to the point that it was wearing the cassette or rings. As was said, if you put the new chain on and it skips under power you will need to replace the rest of the drivetrain.
Once you are full on waxing, you'll find that the entire drivetrain lasts much longer. We have some test drivetrains in our lab with 25,000+ miles on them (all of those miles at 250-600 watts!) and everything still in spec. You can expect a good 10,000 miles from a chain if you are waxing it regularly and easily 2x that from your cassette and rings.
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