Hot Air Gun for Reflowing a Board?
Could this possibly damage the board?
Of course.
What about all the parts?
Yes. It could certainly damage them too, and most probably would.
Are there any other pitfalls that I might encounter or would this method work well?
The problem with this method is that it is inherently poorly controlled. It is potentially able to work and an exceptionally skilled and experienced and well trained operator may be able to achieve somewhat acceptable results some of the time. But most of us would just end up with a work of art or a pile of smoldering slag.
Probablility ~= 1.: Reflow soldering is an exercise in controlled death. Components and board are heated up hot enough and long enough that they are well on the way to destruction. Manufacturers design parts to meet the stresses of this process with an acceptable margin of safety. If you read up on the reflow process in detail, as you MUST have already done to make this question more than idle time wasting, you will have found that temperature profiles - rates of temperature change, holding times and cooling times and temperatures are all tightly specified. If you can manage the sort of control that this implies over the surface of a PCB containing 250 or so components including fine pitch TQFPs then you are wasting your time in your present role and probably want to enroll as a micro-surgeon or Formula One driver or similar :-). ie it's far too demanding a task for this to have any certainty of working.
Probability ~= 0: Not everyone is Wouter - he is an extremely experienced and capable engineer. All that said, it is "just possible" [tm] that a consistent approach, well aligned jig, temperature controlled air source etc may be able to do the job quite well. Finding out could be expensive. Or not. Given the very great success achieved by the toaster-oven-PCB-assembly community and the large amount of on-web information available on this method and the relatively low cost of doing it, I'd expect your TQFP's to thank you profusely for taking that route.
Related:
Spark Fun show you how to do Toaster Oven PCBing - lots of details - MANY photos
Some amateur results
Lots and lots and lots of PCB-toaster-oven ideas
Open Hardware PCB toaster over project
And more ...
Even a small BGA - an instructable
For a double-sided board I do the most populated side with a simple reflow oven (T-962, typical Chinese medium-quality low-price poduct with an awful manual and user interface. before I got this one I used a toaster oven with home-brew temperature control). The other side I do with a paint stripper host-air gun. It works quite well, but
it takes some self-control to approximate the normal reflow temperature curve: I must keep the air gun at ~ 20 cm for maybe a minute (my arm does not like this, and neither does my brain), then move it to ~ 10 cm and move it around for the actual reflow.
the air flow is quite strong, some components 'drift' around the board. I don't know whether this will be more of a problem or less with smaller components (they are lighter, but also smaller and have relatively more contact area with the paste and (later) solder).
My stencils and eyesight are good down to 0805, I did not try below that
some people are worried about ions in the hot air flow that could cause static charges that can damage components. I think that has not been a problem for me, but I am not sure I would have recognized symptoms of this. I live in the Netherlands, so humidity is never low.
An alternative is a electric skillet. I like this method because I can get a good view of the parts with a magnifier as they reflow. I can lower the heat the second the largest part reflows. It's also easy to monitor the temperature with a infrared temp gun for the initial soaking. I have had good results with this method.