I would say go for it, although perhaps you could ask if you could start a little easier. As its not just live spiders that bother you perhaps you could start with pictures and work your way up to a real one.
I totally sympathize, before I had kids I was terrified of spiders, jump across the room, scream the whole bit. As my kids got older I decided I didn't want them scared as well so I grit my teeth and smiled and pretended they were fun little things (!$@#&@$) it took a while ( ok a looong while lol) but a few years later we actually bought our first tarantula, it's strange, I was still nervous of the little ones, but the big ones didn't bother me at all.
We ended up with a grand total of 32, I handled most of them, lol NO ONE handled golly, our goliath bird eating spider, he was HUGE ! , Anyway, I think this is something you need to do for you, it will change your life, no more opening a newspaper or magazine and feeling your heart stutter, no more being frozen with fear at a shape on the wall.
Go for it !