Will keeping my belly "tucked in" or taut help strengthen my abdominal muscles? Are there any negative sides to doing this? I used to do this in high school but gave up doing it when I started working and the sedentary life kicked in.
No. A muscle won't get stronger unless you make it do work: crunches, or keeping a tight core during a lift, for example. I suppose your abs do a bit of work if you just keep them tight, but they'll adapt to that really quickly and you won't see any extra strength or size come from it.
However, in the context of lifting (squats, deadlifts, pressing, cleaning), your abs will be doing a significant amount of stabilization work, and that will make them stronger. Here's a really good article by Mark Rippetoe on the subject of abs.
Also the tag of bellyfat suggests a link between the strength of your abdominal muscles and the amount of fat around your belly. There isn't any.
I don't think anyone is giving you the answer you're looking for. If I understand this question correctly, you are asking about keeping your abs engaged or taut at ALL times. Yes this most definitely works! I started "holding in" my stomach in high school, and I always had ab definition without much effort. Lately, I've stopped and there is a huge difference. I am training myself to start doing it again. Keep your abs tight as if you were doing crunches. It is challenging at first, as you have to train yourself but eventually it becomes something you just do without thinking.