What happens if a solder joint cools before all the flux has evaporated?
Technically, the unevaporated flux will form voids in the solder and mechanically weaken it. Additionally, the non-conductive voids will slightly increase the overall resistance of the connection.

But.

You should be aware of an old saying:


  The military think that solder has zero strength. Hobbyists think that
  solder has infinite strength.


Your approach should incline toward the military philosophy. If slight decreases in mechanical strength are an issue, you are guaranteed to be be counting too much on your solder. Physical strength of a connection should always come from physical aspects. For instance, don't connect two wires by laying the bare ends side by side and soldering: twist them together first. If you're soldering a PC mount transformer to a board, you MUST provide mounting screws. Things like resistors and (non-electrolytic) capacitors are simply not going to stress the joints in normal operation. If they do, you're working in a high-vibration environment, and even counting on perfect joints will not save you.

In a similar vein, solder provides something like a perfect (sub-milliohm) electrical connection, and a slight increase in resistance should not cause any real problems. If you're working at current levels where self-heating might be an issue, you already have to worry about self-heating of the conductors themselves, and you should be looking at purely mechanical (such as crimping) connections. If you're worried about extra voltage drops or changes in effective resistance, you're working at such low impedance levels that you need to be paying all sorts of attention to the circuit details anyways, and letting the flux completely react will be part of your process already.