No, it could not safely travel into unobstructed matter, at least the time traveler himself didn't think so.
'The peculiar risk lay in the possibility of my finding some substance in the space which I, or the machine, occupied. So long as I travelled at a high velocity through time, this scarcely mattered; I was, so to speak, attenuated—was slipping like a vapour through the interstices of intervening substances! But to come to a stop involved the jamming of myself, molecule by molecule, into whatever lay in my way; meant bringing my atoms into such intimate contact with those of the obstacle that a profound chemical reaction—possibly a far-reaching explosion—would result, and blow myself and my apparatus out of all possible dimensions—into the Unknown. This possibility had occurred to me again and again while I was making the machine; but then I had cheerfully accepted it as an unavoidable risk—one of the risks a man has got to take! Now the risk was inevitable, I no longer saw it in the same cheerful light. The fact is that, insensibly, the absolute strangeness of everything, the sickly jarring and swaying of the machine, above all, the feeling of prolonged falling, had absolutely upset my nerve. I told myself that I could never stop, and with a gust of petulance I resolved to stop forthwith. Like an impatient fool, I lugged over the lever, and incontinently the thing went reeling over, and I was flung headlong through the air.
http://www.gutenberg.org/cache/epub/35/pg35.html (The Time Machine, by H. G. Wells )