Considering that this is what that little boy looks like eight years later, I'm gonna say no
That's not a valid reason for thinking the characters aren't supposed to be the same.
Counter-argument: Edward Furlong, Nick Stahl, Christian Bale.
Shoot, how about
: Sean Connery, George Lazenby, Roger Moore, Timothy Dalton, Pierce Brosnan, Daniel Craig.
Counter-counter-argument: There's no evidence to suggest the kid is supposed to be Blake, either.