If you don't move the bridge, the effect will be that the guitar won't play in tune. The placement of the frets on a Stratocaster-replacement neck assumes that the scale length of the strings (the distance from the bridge to the nut) is 25 1/2". You'll need to recreate that same scale length in order for the frets to align correctly with in-tune pitches. So here's what to do: mount the neck to the body, measure 25 1/2" from the nut, and mark that spot. @MattB5 is correct: that spot is likely close to the strap button on the bottom of the body. That's where you want to mount the bridge. Make sure you line everything up correctly so that the strings remain parallel to the neck.
Assuming that all goes well---you mount the neck correctly and move the bridge to the right place so that everything plays in tune---the effect on the guitar's tone should be interesting. On the one hand, you'll be dramatically increasing the scale length of the instrument. This will increase the tension on the strings and brighten their sound. See this question for more discussion on the effect of scale length on a guitar.
On the other hand, the pickups will be in different locations relative to the strings, and this also will have an effect on the tone. Think of the difference between a Strat's bridge pickup, middle pickup, and neck pickup: as the pickups get closer to the midpoint of the strings, the tone becomes rounder and less twangy. Your custom guitar should exhibit even more of that trend, since the pickups will be even closer to the midpoint of the strings than on a normal Strat.
So the increased scale length should brighten the strings and clarify the low end, while the shifted position of the pickups should make the tone rounder and less bright---in a way, these two effects cancel each other out, but my guess is that instead, you'll have a guitar with a unique tone: both clear and well-defined but also round, without the harsh twangy sound that Strats can sometimes have.
