The cleaver shaped head (I can't remember the other name for it right now) on its own does not make it a Baroque/Period bow. These were more common on period bows, but some modern makers are making otherwise "modern" bows with them just as a stylistic choice.
Open frogs (I'm assuming you are referring to frogs that do not have a pearl slide or ferrule on them) are much more common on Baroque/Period bows than modern bows. The pearl slide is more of an artistic choice; it does keep your hand out of the hair and add some weight to the frog, but doesn't have a lot of functionality. The ferrule is highly functional.
The ferrule adds a significant amount of weight, but is really there to allow the use of a spreader wedge. It holds the hair in place, and makes sure it is stretched from one side of the ferrule to the other to create an even band of hair. With an open frog, there is nothing other than the plug in the mortise spreading the hair. Unlike the tip of the bow where the mortise is the desired width because of the concave curve of the side of the frog, the mortise cannot be as wide as one would like the band of hair to be on a typical modern bow. If that is confusing, think of it this way: the hole that the hair goes into needs to be narrower than the most narrow part of the frog which is more narrow (especially on a German bow) than the desired band of hair.
Without a ferrule, you either have to have a wider frog, or a narrower band of hair. Not having a ferrule also makes playing on the side of the hair (where you roll your bow so you aren't using a flat full band of hair) more difficult, as the hair is free to move and redistribute itself; you are more or less always playing on a full band of hair. If that is one of the ways that you create dynamic/colour contrast, you don't have that in your wheelhouse anymore.
As previously mentioned, the head shape and pearl slide don't change the sound of the bow, the ferrule is functional and does have an impact, but the "important" part that makes a modern bow modern is the camber. Having a concave camber in the bow allows the bow to bounce, grab the string, and "bite" or "attack" in a different way than on convex bows. The curve is going to greatly impact the technique you have to use, which in turn impacts your sound.
Yes, you will be judged. This is the orchestra world, where we are still fighting over French vs. German bow grips, 4ths vs. 5ths vs. 5 strings vs. extensions, new vs. old instruments, and there even was a thread about playing "blonde" instruments and which colour of finish is appropriate in an orchestra a while ago. Every possible choice you make about your instrument and bow will give someone a reason to judge you, and this is one of those cases where you would be stacking the deck against yourself. Unique is not an asset in an orchestra. If you are auditioning for an orchestra that plays period music on period instruments and/or bows, it would be an asset. If you are auditioning for a "normal" orchestra, you are giving the panel the "he's the guy with the weird bow, right?" reason to hire someone else.
If this is something you are interested in pursuing on your own time, or you have an ensemble/opportunity in mind where it would be appropriate, by all means go for it. If you are considering hitting the audition circuit, I would leave it at home and bring a "normal" bow.