I don't see why not.
You can actually make your own sensitizer and add it to regular glue, so I imagine it would be the same if you use a store bought sensitizer. You might have to experiment with your mixture ratios though since emulsion and glue have different physical properties. (I've never bought emulsion though, so I could be wrong)

Homemade Potassium Dichromate sensitizer is mixed with PVA wood glue (I like Elmer's Carpenter glue)
Any wood glue (or white glue for that matter) should work fine. Just be sure to get the "Interior" type. I've tried several other glues and "exterior, waterproof, all weather" grade glues usually cure without any exposure time, ruining your screen. Even Mod Podge cures without exposure. Ruined my very first screen that way!

Wood glue is thicker than white glue, but it's still pretty runny, especially after adding sensitizer. So before I add sensitizer I like to mix about 10% corn starch to the wood glue to thicken it up a little. This will prevent drips and drops from forming on your screen as it dries (a fan also helps)
I'd actually like to thicken it up a bit more, but I think 10% works just fine. I'll have to experiment.

Here is the ratio I use:
1 part corn starch
10 parts glue
2 parts sensitizer

Anyway, I'm glad to hear you're breaking away from the embroidery hoop and mod podge fad. Unfortunately, people often marry "cheap" with "easy".
Making a good screen isn't expensive, it just takes more work than a trip to Walmart craft department!
Hope this helps. Contact me with any further questions.