I definitely don't think fan pressure has anything to do with these signings. We were after a striker, with two bids made public and the injuries to Merts and Gabriel made it obvious a new player was needed there in addition to Holding.
If Wenger is seen as someone who doesn't care about, listen to and condescends toward the fans, then a couple of matches with a small section up in arms wouldn't have made a difference to him. He's stubborn as a mule and makes these decisions on his terms only.
The problem, as always, is the timing of the signings. We should've had these guys in and ready for the start of the season. Not two (probably three) games into it. There is also an international break after this weekend, which means even less time for Mustafi to bed-in with the team, which is really needed for the defence.
If, as the fan article about Perez indicates, he is similar to Vardy then hopefully that does lean toward a change in style and feels like a more considered purchase if he is a similar style of player. All of which remains to be seen. Either way, having another striker option can only improve us, even if it is marginally at worst. That said, even a 25+ goalscorer wasn't going to be our saviour. We all know we need a new manager to make the best of any squad at the club. But, we also need more goals from midfield. It's pretty barren back there and until we get a better spread across the team, our tendency to be wasteful will be more heightened.