Re: it's already doing 17.46 km/hour
"When you're going that fast, doesn't time slow down or something"
yes but the amount is negliglble. you'd probably notice if you're receiving radio signals that are supposed to be xx.xxxx Mhz, but end up being xx.xxxy Mhz [that kind of difference].
As I recall, on one of the Apollo missions, they had an atomic clock or something similar on board the spacecraft, and they actually measured the time difference. Since they were moving at ~50k MPH for the trip to/from the moon, there would be a measurable effect, even though it was pretty tiny. But, the scientists involved in the experiment DID find "that difference" and announced that Einstein WAS right. It was definitely worth doing, yeah.
You can figure out the effect on time when you consider that if you're travellng at 1/2C, then [simplified] from YOUR perspective, light still moves at C, which means that for you, time effectively moves 1/2 as fast as it is for someone who's not moving at all. It's actually more complicated than that, but discussing all of the details in here would be TLDR and *yawn*. NOT mentioning that would invite the anal retentive howler monkey types to nit-pick every word.
anyway, ~18km/sec compared to ~300,000 km/sec is a pretty small change in the flow of time, but it's in the neighborhood of 1/10,000 [unless I made a math error] so radio frequencies would be shifted in a measurable way [as I already mentioned at the top] but that's about it. What's interesting, however, is that the shift would probably be TWICE what doppler alone would cause, because the relative time would affect the RF oscillators, which would put out a lower transmit frequency, which would then be further time-stretched by the doppler effect as the craft moves away from earth.
[gravity wells, as mentioned earlier, notwithstanding]