It will expand and dim, but two weeks of expansion where it is most visible will only give it 2 light weeks of radius. Beetlegeuse currently has only about a light hour of diameter, which is huge, but we'd expect something about a hundred times as wide. Keep in mind that at 640 ly the sphere has a surface area of 5 million square light years, or 250 million square light weeks, and it would itself only take up about a dozen of them, or about .002 deg². Whereas the Sun and moon are .2 deg², so basically a tenth as wide and probably brighter than the moon but much dimmer then the sun. Most stars appear a set size to use because they are way below our visual resolution, literally a dot the same size as the other just brighter or dimmer, I'd have to run the numbers but I'm pretty sure all stars beyond a light year in proximity would be well under the size of a single 'pixel', and thus presumably need to expand a lot before they'd even register as a bigger rather than simply brighter star.

Now the things get huge, covering whole swathes of the sky but usually they've dimmed and cooled below human visual sensitivity by then, the thing would be a giant monster smeared across the night time sky for decades after in the infrared range. We should be able to see it at night for many months afterwards too, getting bigger and dimmer, and if it's .002 deg² at 2 week it would be .2 (Moon/sun sized) at 20 weeks and should still be visible to our naked eye at night. The crab nebula was visible for three weeks of daytime and 2 years by night and it took place 10 times further away, so I'd guess we'd actually be able to see Beetlegeuse for some months during the daytime and probably several years at night, if so it would have swelled to take up perhaps as much as 100 times the area of the moon or sun, though very dimly, by then.