No they don't, it's a mixed picture:
Southampton signed 8 at £32m in their first PL season.
Bournemouth signed 11 at £41m
Palace 18 at £26m
Burnley 7 at £28m the second time around
But as you say there are others that did the same and went down.
All of top flight quality:
CB (if Goldson's going out on loan)
RB with pace
Right midfield/winger (cover for AK)
Striker with pace
Striker who can hold the ball up and score