Kristi:
Congratulations! I can feel your excitement from here!! Maybe the more experienced runners (just about everyone but me) will chime in, but here's my two-cents worth: I would think it would be fine for you to participate in the 5K, but maybe keep in mind that you might not be ready to run the whole thing. There's no shame in a run/walk. At this point, it's FINISHING that is the most important thing
. I am planning to run a 5K in April (I'm only ahead of you by two sessions, I just completed W1D3). Prior to that 5K, there is one in March that will participate in with a goal to complete a 1 mile run and walking the remainder.
Maybe you are one of those "over acheiver types"
that wouldn't be satisfied with that, but I'm more the type to follow a program just as it is laid out, so I will be running only three days per week and doing some strength training on two-three of those off days, with one-two days of rest each seven day period.
Other than being concerned about over-training or burning out, there may not be anything wrong with going about it the way you propose. Just listen to those who have more experience and lean on their wisdom.
It's really easy to get all excited about this, though isn't it?
Again, BIG pat on the back for completing W1D1 
Sorry about all the smileys, too! 