I think my main point is: if Clapton played a hot rodded $300 guitar through a nice amp, I don't think you'd be asking "is he playing a souped up $300 guitar placed through a nice amp?"... 

 
Yep, I agree with your point Keith.  Playing your Squire, Clapton would still sound like Clapton and he would squeeze every bit of tone out of that Squire, that the instrument was able to give up.  However, blind folded, he would still know he is playing a Squire.  If I remember right, he took the best parts of 3 Stratocasters to make up Blackie, so he is obviously particular to the feel and quality of the guitar. 
 
My son has that same Squire in a Gold finish.  For the money, it is a very fine crafted instrument.  I also own an American Deluxe Strat and it in no way compares to the Squire.  It would take more than a pick up change to rival the Deluxe.  All of the electronics would need to be upgraded.  The bridge would and nut would need to be changed out.  To come close to the feel and playability of the neck, the neck would have to we swapped out for a Fender or Warmoth....and then the body would still be basswood.  If I were to record the 2 instruments, distorted, you probably would not be able to tell the difference.  EQ and compression can do wonders.  If you sat next to me while I played through an amp, if you have a discerning ear, you would most likely hear differences in the details of the tone, pick attack and sustain.  The main difference IMO, is the feel and playability in the hands of an experience guitar player.  Now, would I buy the American Deluxe for my 16 year old son.......NO.....he would never notice the difference.