In terms of the talent of their team in a vacuum, I'd say they're about where we were at the start of 2009-2010 - generally solid at the back, solid midfield with the potential to improve and an acceptably potent frontline, although I'm unsure if Sandro Ramirez and (possibly) Giroud can be their Defoe and Crouch, per se.
However, when you return their team to the context of the Premier League in 2017, they're nothing too terrifying. A full-strength Everton side would probably look something like....
Pickford (GK) - Funes Mori (CB) - Williams (CB) - Keane (CB) - Coleman (RWB) - Schneiderlin (CM) - Gueye (CM) - Baines (LB) - Sigurdsson (AM) - Klaassen (AM) - Ramirez/Giroud (?) (CF)...
...in a 3-4-2-1 formation. Reasonably solid backups can come from Joel (GK), Holgate and Jagielka (both CBs), that RB from the England U-20 team (his name escapes me at present), Davies, Barry and Besic (CMs), Rooney and Mirallas (AMs), Azza and Lookman as wingers and Dominic Calvert-Lewin as a forward. And that's assuming that Barkley leaves - to us, most probably.
It's nothing that scary. There is a notable lack of pace in that side, for one, and many of their players can be described as 'workmanlike', as opposed to spectacular. That side screams 'solid' to me, but it doesn't scream 'threatening'.
I don't think Koeman will have too much of a problem integrating players *reasonably* quickly - he did it before at Soton, twice, after having to bring in a lot of sub-par players to replace genuinely good departures. And he got results both times, so that's not in doubt. They might have a rough start (given that they play us, United, Chelsea, City and Stoke in their first five games, iirc), but I think they'll knit together after that. But what is in doubt is the potential of this side - a lot of the players are solid, but they're at their peak already, and when put together I don't think they'll deliver some magically magnificent season where individually they've all proven to be roughly upper mid-table Prem players over the years.
I think, in the end, they'll do a solid job - like our side in 09-10, they should probably be pushing for somewhere above 65-odd points, with 70 being the absolute dream. But unless Koeman has some tactical revolution up his sleeve, I don't think they can get better than that with the team they have now.
And whether that points tally will be enough to get them a CL spot is a *very* open question - especially considering the arms race that the Top Six (excluding us) are engaged in. For every solid signing Everton make, United, Arsenal, Chelsea, City or Pool go out and drop 40-50m at the drop of a hat on someone better. And given that they're all also headed by world-class managers, it's unlikely that the dominance of the Top Six relative to the rest of the league will decrease unless some black swan event majorly changes the outlook of one or more of those teams.
Given those realities, their spending so far isn't likely to change the paradigm in an unexpected way. Judging by their spending so far, they're going for solidity over instant ambition - start with a solid base and build upwards. It's probably the right move, and provided that their net spend stays high over the next few seasons, they should build themselves up into a genuine Top Four contender in that time, and then move for the title from there.
But it isn't going to happen this season, I think.