Do Corgis shed?  Yes.  If there were a word that meant, “you would have less hair in your house if you adopted a woolly mammoth,” then that would be more descriptive that merely saying Corgis shed.  I have combed out an old fashioned, full sized, grocery store paper bag of hair out of one Corgi in one grooming.
 
Do not despair if you have your heart set on a Corgi.  It you are willing to put in a good 2 weeks a year on hair patrol you can stay ahead of this menace.   Ever spring and fall when your Corgi starts to look like an unkempt lama take your Corgi outside.  I cannot stress this enough.  Grooming them indoor is just silly.  The fur will get everywhere despite your best efforts.  Releasing the hair outside, at least allows the birds to use it.

Step 1.  Brush your Corgi thoroughly.  After you have brushed the Corgi, comb them.  Get every last loose hair off of them.  Be careful in your zealous not to be harsh in your brushing/combing.  After all of your precious Corgi is under all that fur.  So be firm in your brushing, but don't bruise or scrape the Corgi’s skin.

Let your Corgi run around at this point a bit.  Sitting for this sort of grooming makes them tired, sore and bored.  They need to stretch those little legs.  If your Corgi is particularly woolly you may want to spread this phase out over two days.

If any dog or cat has mat’s in his hair and you wash him before removing the mats, the mats will tighten up during the wash.  Don’t just cut out mats.  You must be VERY careful.  The mats sometimes pull skin into them, so if you cut the mats, you cut the skin.  It is hard to see the skin in the mat.  If you have any doubts, take him to a professional groomer.

Step 2.  Bathe your Corgi in warm water.  Note: that is warm not hot.  Warm water loosens the hair from the hair follicles.  That allows the rest of the lose hair to slip free easier.  Suds him up and rinse him twice.  Then apply a high quality cream rinse.  Rub it in good and then rinse it out.

There are little screens you can put over your bathtub drain to catch the hair.

Do not skip to this step without having removed all the hair you could first.  There are two reasons for this.   One the amount of hair would be overwhelming, and two it just won't work as well.  The wash technique will not work as well with all that extra fur in the way.
 
Step 3.  Dry your Corgi and repeat step one.
 
Continue the daily brushing/combing for the remainder of the week.  By the end of the week, you should have the hair under control and not everywhere in your house.