An even larger problem, if you don't have the top section of your mast plugged both top and bottom, is that the mast fills with water making uphauling/waterstarting pretty much impossible (you are at the wrong end of the lever).
So, by overall importance, here's my take on the value of plugs:
Top plug in the top section "Criticallly important.
Bottom plug (above the ferrule) in the top section: Pretty important
Top Plug on the bottom section (inside the ferrule) : very important
Bottom plug above the mast base in the bottom section: not important at all.
The mast base works as a "plug" of sorts, and as suggested, unless you turn your board over for some reason, in the water, there's no way for water to get into the bottom of the mast.
AND any water that gets into the lower section of the mast can run out the bottom if you do not have it solidly plugged.
Hope this helps,