There's two questions here:
- What's a successful strategy for a senior leader to do when he's away?
- What will work in your specific company and what, conversely, are career-limiting behaviors?
The latter point is not something we can answer here, as it's really a case-by-case situation for the business, the culture, the company, and even your boss' specific opinions. You're only going to answer that by both having a frank conversation with your boss AND by watching the outcomes of the decisions you make.
In terms of the former - my answer is that there is always a cut off line. Somewhere between "where are the paperclips?" and "help, the city we work in just had a major catastrophe and we are doing major disaster recovery" is the line between you being bothered while away and the situation being addressed by someone else.
The more senior you are as a leader, the more it becomes YOUR job to figure out where that line is, and to train the organization around you (both beside and below you) to act accordingly. Some of it is likely to be business related - how much does the company risk, if you are NOT the person who handles this? Some of it is contingency related - what is the risk if you are the ONLY person who could ever handle this? Ideally as a senior leader in a healthy firm, you are NOT making yourself indispensable, you are growing the organization so that a new leader is ready to take your place by the time the business has grown to the point that you deserve a promotion. If no one is available to be your deputy while you're gone, I'd say you need to consider whether you are addressing the skills within your team appropriately.
In terms of scheduled events - it's probably time for a conversation on how much advance notice should be given (for either your vacation or the company's event) vs. the expectation of a drop-everything all hands on deck type of gathering. Generally for a "we could book this at any time" type of occasion, there's a reasonable expectation that if everyone is expected to be there, you'll be told to be there far ahead of a reasonable time for booking time off. And also that such events will not occur so frequently that you can't possibly take a vacation. But this is a factor of the company, the size, and the nature of the event.