EI definitely cares if you go on a trip: you are not available for work. Do they care if you go to Calais for the day or Bangor for the weekend? No.
Florida for 2 weeks, definitely.
HOWEVER, would the american border guards report anything to them? Never! They don't give a hoot about any Canadian institution.
They are all about stopping "evil doers" ;-)
Unless they are carrying bloody chainsaws, that is !?!
Frequently, people with no visible means of support who can afford to travel are up to no good. I spent a couple of hrs waiting for a buddy of mine several years back while they decided if his claim to be self employed was legit (It was, but who thinks to bring proof of that on vacation?). I have been asked where I worked a hundred times there I bet, it's just one of their qualifiers to weed out those who warrant more scrutiny.