With industrial testing and equipment, it might be possible.
As a practical matter, for a home cook, no this is not possible.
The reason is safety: long term canning requires ensuring that the product is shelf stable and safe for longer term storage, which means killing or preventing the growth of all pathogens that might be in the food. Possibly the most difficult and dangerous to manage is botulism, whose spores are fairly ubiquitous, and which can grow in low-acid, low oxygen conditions—the exact conditions that prevail inside a canned product like this.
Even though your dressing may be acidic, the entire volume inside the jar including the pasta and other ingredients will almost certainly be insufficiently acidic to inhibit botulism growth.
The only way to know for sure that a recipe (and the associated canning methodology) is safe is with expensive industrial testing (the kind food companies use when bringing new products to market), or to exactly follow a recipe designed by a reputable source such as a University Extension program.
Unless you can find such a recipe (I failed to do so in a quick check, but it is hard to search for), you should not proceed; but even if you do, you would have to follow that recipe, and not use your own.