Can I launch Fallout: New Vegas via Fallout 3's launcher on Steam?

As others have mentioned, the Tales of Two Wastelands (TTW) mod is a mod that brings the content of Fallout 3 into Fallout: New Vegas. You have to start Fallout: New Vegas in order to get it to work.

What is Tale of Two Wastelands (TTW)?

Tale of Two Wastelands (TTW) is a project that seeks to merge the content from the popular video game Fallout 3 into the more modern game engine of Fallout New Vegas so that both games can be played in the Fallout New Vegas engine.
_{- TTW FAQ}

If it was possible to use TTW mod and the Fallout 3 launcher, you would need to install the TTW mod into Fallout 3. Even if we ignore how much stuff would break when TTW loads up and starts looking for New Vegas items and objects, this would also just bring all the Fallout 3 content into... Fallout 3. No New Vegas stuff would carry over, it would be an exercise in futility.

The only reason I can conceive of doing this, is an attempt to preserve your F3 FOMM settings (or to use a mod that's not compatible with NV.esm, without which TTW won't work anyway). You have to import all that into NV's FOMM/GeMM list.

Here's the important part of my load order for NV, with TTW, using NVSE to launch it: