In theory, it costs nothing to ask. The worst that could happen is they say "no".
However, were I in that situation, my view would be as follows:
If the company will reimburse me for travel expenses they will tell me - and they will spell out exactly what is covered. If they don't tell me a cab to/from the airport on my side is included, I'm going to assume that's because their internal finance policy does not cover it.
I then have 2 choices. I can swallow the cost myself- justifying this decision by the fact it's not a huge amount relative to the potential salary on offer. (You have to spend money to make money!) Or I can take a chance that they've forgotten to mention this (unlikely IMO), ask them to confirm and maybe save myself some money. My concern would be that in doing so I would paint myself as somebody who would be a demanding, high maintenance employee, who's never happy with anything the company do. However accurate that is, I don't want them to have their decision made before I even set foot in their premises.
That's just my 2c.