No, higher octane fuel burns at a lower temperature and is harder to ignite. That's the whole point of it. If it's harder to ignite, it's less likely to be ignited by temperature and pressure in the cylinder (as opposed to the spark). When fuel ignites without a spark (on the compression stroke), it's called preignition or detonation, which can ruin your engine. That's why octane rating is called an 'antiknock index'.

Higher octane fuel that is harder to ignite is less likely to cause detonation in a hot cylinder. That's why it's important in high compression engines-- compression = temperature. 87 octane would probably cause detonation in a 11.5:1 compression engine, but it's safe in a 9.5:1 engine.