You can, but you shouldn't.
You will have to pre-fold every sheet, which costs a lot of work (and thus cost wages) and you will not get every page folded properly. Plus, chances are you'll have to redo a fair amount of sheets because you put in 1 of those 4 'pages' the wrong way. Plus the risk of tearing, crumpling, paper jams, etcetera.
It's a lot of work for a less-than-stellar result.
If your company needs to do a lot of this kind of printing, the printer will pay itself in less time spent on menial labor. (measurable benefit) On top of that, it'll save a lot of frustration. (immeasurable benefit)
As usual, being on a low budget means making compromises. In your case you'll have to chose between looks, waterproof, and low overhead.
If you want looks and waterproof, go to an external printer and pay more per page, or invest in an expensive printer yourself; Expensive but best. If you want looks and affordability, you'll have to agree on less waterproof prints. Cheap, but goodlooking. If your line of business demands durability; go for practical and affordable.
Alternative: outsource, but not entirely.
If your company doesn't need to do a lot of this kind of printing, just go to a copy shop. They'll have a couple of $XXXX machines there that'll work fine for your purpose. It'll cost more per page than having your own machine, but at small runs it shouldn't be too big an overhead. Having the shop do the printing but doing the binding yourself should still be a bit cheaper than Lulu.
Note; Lulu isn't a generic 'printer', but aimed at publishing books. If you just need brochures printed, look up a local offset/digital printer. 5 copies; copyshop, 50 copies, digital print, 500 copies; offset.
If you do end up going there fairly often, you can ask for a discount or reconsider investing in a printer)
Alternative: go with inkjet anyway.
I don't know what the use case it, but there are inkjet paper types that are somewhat water resistant. Many photo papers for example. If it's just the occasional drop of rain, this could suffice. If you're making diving maps (are those a thing?) then of course you need something more heavy duty.
But if you can live with water-resistant instead of water-proof, you can pick up a decent A3 inkjet printer for a few hundred dollars. I've personally been looking at purchasing a Brother due to their low ink prices - but you should do your own research. ;)
Alternative: use a different binding method.
Something like Comb Binding or Coil binding will work just fine when you have an A4 printer. It might not be the look you're hoping for, but it's easier to homebrew than saddle stitching and I think it's a bit more durable too.
If you want something more stylish, you can try Japanese binding. There's a bunch of interesting patterns if you want to get creative. You could also go for screw&post binding, which can be either with spine or without spine.