Not that useful.
If you're a True Believer who is intent on conducting business in bit coin whenever possible, nsn's answer shows that there are destinations and businesses with which you can transact, yes. As this recent WSJ article demonstrates there are travelers making a concerted effort at it. The article also includes links to a few notable travel agencies.
However, the articles subject also notes that using Bitcoin has been "consistently inconvenient and occasionally frustrating," and cites travel plans that include carrying an extreme quantity of provisions - including gasoline for their car - for fear of not being able to acquire them with Bitcoin when pressed. Put in other terms, BITCOIN IS NOT A VIABLE ALTERNATIVE FOR EMERGENCY FUNDS.
While you can plan a trip and book lodging that will accept Bitcoin, the situation cited in he question, losing a wallet while abroad, is one in which you need flexibility above all else - which bit coin offers very little of. Converting Bitcoins into other currencies - especially on short notice, and in economies with which you are unfamiliar is... non-trivial, to put it lightly. If you're unable to convert your magic beans into local currency, you'll find your options become very limited, very fast. Furthermore, a large amount of Bitcoin spending and management is dependent on computer and internet access. Losing your smartphone can become as, or more, crippling than losing your credit card. While you can make 'paper wallets' in preset amounts to hand people to conduct a transaction, you need to prepare these in advance, and it requires access to yet more technology in terms of a printer.
TL;DR: anything you can do with Bitcoin, you can do more conveniently, in more places, on shorter notice, and in most cases, more cheaply with real money in normal bank accounts or cash. If you don't have an ideological reason to do so, there's no reason to use Bitcoin.