This isn't my cup of tea, but a friend of mine ran one like it that was apparently successful way back in 2E. My comments:
1) I don't think it works for a real long-term campaign. I mean this not to be offensive at all, but it revolves around a gimmick. Also, it runs the risk of devolving into Army of Darkness pretty quickly. That doesn't mean it has to be a one-shot, but I'd plan it for more like a couple of related adventures. Also, as they level up, the idea of the campaign -- that they would be "normal" -- starts to evaporate. Normal people can't take multiple arrow shots to the chest without blinking.
2) Why wouldn't magic work with them? Why add that element? What work is it doing for you? If one of the PCs wants to learn magic, I don't see why you wouldn't let him.
3) The people you're talking about aren't exactly "normal." When my friend ran it he took a page from the ol' D&D cartoon show and just had the actual people get sucked into it. So, they were about as capable as ordinary college students, with a little bit of creative license. A Green Beret or Bear Grylls are themselves on par with adventurers, most likely. And, there seems to be a bit of disparity between them and the Engineers.
4) The basic question -- can they survive and thrive? -- seems to me to be pretty much yes. If they make it through the adjustment period they can do awesome things. Even just a steam engine would be revolutionary in a fantasy environment. You're sort of running headlong into the tippyverse here, so be warned. A modern-day engineer is going to look at all the things a D&D mage can do and come up with creative, wacky things to do with them. These sorts of things don't come up in a fantasy game, imho, b/c of the genre conventions. Naturally, this campaign idea is changing said conventions.
Hope that's helpful.
The thing with they not being able to use magic is to not get caught into the D&D Magic Arms Race. Magic is so powerful, that when you have access to it, it kind of defeats the point of having access to advanced technology. In my head, the campaign, to work as intended, needs to be a sort of Magic vs Technology, and for that to be true, the heroes out of time have to make due without access to *any* magical equipment.
On the disparity between the engineers & the green beret/bear grylls... The descriptions may be kind of misleading, but i didn't meant for the engineers to be any less powerful than the green beret or bear grylls. It'd probably be best described if i said Tony Stark/Leonardo Da Vinci. These are not your run of the mill college graduates, they're the best on their field. They're asian.
Taking multiple arrow shots to the chest and surviving... Yes, this would be the most difficult point to balance out with "reality". But something's gotta give, and the system has it's constraints, so the HP system and creative storytelling would have to make due. The party would probably also need Dr. House, too, since they don't have access to magic.
As to modern stuff needing modern machinery in order to be made... This is not entirely true. Many weaponsmiths work with tools some would call archaic. In the internet, one can find many designs of improvised "Zip guns" made with pipes and tools repurposed... The Anarchist's Cookbook is a good example of the kind of stuff i'm talking about.
On the downtime, the engineer & the chemist could also set up a small scale factory, with their knowledge. Modern day technology about forging of metals, identifying of materials, etc... Rudimentary flintlock pistols can be made out of wood, with few parts made of steel. High explosives in suficcient quantity pretty much go to the same level of 9th level magic, too. Nitroglycerin isn't actually difficult to make, just extremely dangerous. If you can get a bunch of peasants to handle the dangerous part, you can make batches of the stuff and then stabilize it with Sawdust to improvise Dynamite. Dystilling of tar to make plastic, to serve as a precursor to plastic explosives is also a doable thing.
The HARDEST part for the adventurers, in the scenario i outlined, i think, would not be mustering offensive power, but defensive power. Magic works so much better in that regard, with so much fewer expenditure of resources and time, that technology gets left behind so much. Not being able to fly is also a very significant setback. This wouldn't be noticeable in the first few levels, but would quickly become more than a nuisance past 7th level or so.
So, in a nutshell:
> Introduce Dr. House to the party, so they have access to the highest form of nonmagical healing. The party lacks a medic, and would die quickly without access to magical healing.
> The chemist needs access to a form of Craft (Chemistry), that works similar to Craft (Alchemy) but needs no magical knowledge or magic use.
> The adventure can't go past mid-high levels due to lack of defensive power. Once most enemies are able to become invisible, teleport around everywhere, fly around everywhere, and tell the laws of physics to shut up and go cry in a corner, technology alone can't handle it. (unless it's so advanced it's like magic).
This sounds about right?