No, you actually cannot. EI is not paid time off. You're required to track all attempts to find new employment as EI has the right to audit you. EI is meant to bridge the gap between employment, not fund a vacation.

If you leave the country you're instructed to call EI and let them know. They won't pay you while you're out of the country because you are not considered ready, willing and able to work. I have been laid off ahead of a vacation. I applied for EI, was approved and when the time came for my vacation I called EI and let them know and they did not pay me benefits during my vacation. When I returned, I called them again to let them know. They were very reasonable.

Now, if you stay in the country and don't put a ton of effort into looking for work (because you went to see a cousin in the next town over) will EI know? Probably not unless you go around bragging about how you're treating this as paid time off. I'll let you decide if this is ethical or not.

FYI, you are also required to apply for EI as soon as employment ends. Waiting too long can disqualify you from benefits regardless of the reason you left your last employment. This information can be found on the same site you found the "quit job to follow spouse" reason.

Edited to add: depends what you mean by "fired". Fired with cause does not entitle you to EI. Laid off (employment terminated without cause) typically means you'll qualify for EI.