Yes, I'm pretty sure that is correct. You would also take off the vowel from whatever the preceding word is, in this case, "senz'olio" as opposed to "senza olio." Maybe I am wrong, as shown by Nitram, but I think this is a consistent rule. Keep in mind though one, that most of us are learning, and two, that google could be wrong.
The reason why "senza olio" is not correct for the "type what you hear" exercise is that she ACTUALLY SAYS "senz'olio", which is why on that specific exercise it doesn't accept "senza olio" (despite the latter also being correct.) And our task to to write exactly what she says. Hope that helps.
I had to do a microphone test with this and it just wouldn't recognize it. Must be a bug. More generally though I am confused when and when not to use a contraction. It seems that sometimes a vowel gets dropped when in other cases it does not. Are there any clear cut rules or does it all come down to euphony? Please does anyone know? A Google search for many variations of the same question yielded no answers. I am hoping my luck will be different here! Please help!
Its only correct if you connect them. These romance languages dont like glottal attacks like at the beginning of "olio". Its the same in frenh and everywhere, its not as smooth to the ear, thats why you put the apostrophe. Plus its too easy to get stuck on these tiny details here. The fact is, NOBODY talks like this "senza olio" in real life youre never going to hear it or say it. Its just part of the culture