I think bringing it without a heads up to the host will probably be perceived as rude.
I might also frame it as "My kid has problems with <insert ingredients here>. Do you know if there will be veggie/fruit/blah choices or should I bring my own? I didn't want to offend you, it's no problem bringing our own stuff, we are used to it, but I wanted to let you know so it wasn't a suprise!"
As people get to know your family and you stay in touch, I think you will find good party throwers tend to think proactively if they know your family has an allergy/sensitivity.
One of DD's classmates is GF and dairy free. As it happens I too had to go GF for awhile last year (part of an elimination diet thing), so I knew of an AWESOME source that has beautiful, scrumptious, gluten and dairy free cupcakes (with fluffy icing!). So after I sent out the invitations I also sent out an ingredient list for the cupcakes to classmate's mom. If there was something in there that she couldn't have or if she prefered to bring her own food it was cool (because I wouldn't have a problem eating those cupcakes, actually my kids/hubby wouldn't either because they are great and not gross or weird tasting like a lot of GF "replacement" stuff, at least IMO). Classmate and mom were thrilled, I didn't realize that mom was also sensitive to gluten, so even mom got to have a treat at the party (I bought a pack of two) which she doesn't normally, and she has a new brand that is safe.
So my vote would be to communicate with your host and give her a chance to take care of you. Lots of people don't mind and enjoy going the extra mile for guests, or won't mind at all if you bring your own stuff with a heads up.
Also, please don't judge people who hold parties at Mickey Dees or whereever. Depending on the area you are in, these may be the only indoor venue they can afford, because most of the time they are free or extremely low cost, have ample parking, and are in a somewhat centralized location. Not everyone can afford to rent a community center room or a more upscale venue, not everyone can accomodate people at their house. So I would really caution against stereotyping what the parents are like based on where they hold the party. Because they have it at CEC or McD doesn't mean that they don't give a rip about nutrition--it might just mean that they want to invite all their friends but can't do a house party, and the food/place is within their expense range or they know it will entertain the kids easily, and they're doing the best they can. If it offends your sensibilities to the point where you're going to look down on the hosting parents or families, it's probably kinder to just not go, KWIM?