It's probably worth pointing out that an RTX 2060 is typically only around 15-20% faster than a 1660 Ti, so don't expect to get massively better performance out of it. For example, if you are getting 60fps in a particular demanding game, a 2060 might move you up to around 70fps at the same settings. And that's assuming that other hardware, like your CPU, isn't what's primarily limiting performance in a particular game, in which case the performance gains might be even smaller.
The 2060 additionally features some hardware support for raytraced lighting effects in the handful of games that support them so far, but enabling those generally causes a big hit to performance, and it's questionable how well this first-generation RTX hardware will cope with raytracing in future games targeting newer hardware.
Perhaps most worth noting, you have a 1080p, 60Hz monitor, meaning it refreshes the image only 60 times per second. So if you are aiming for really high frame rates in competitive games at 1080p resolution, you might be better off spending the money on a high-refresh rate 144Hz monitor instead, as frame rates substantially higher than 60fps will not look much different on a 60Hz screen. And a 1660 Ti should already do a pretty good job pushing at least 60fps at high settings in nearly all current demanding games, and a fair amount more than that in less-demanding esports titles.
Also, the high-end 20-series cards launched the better part of 2 years ago, and the 2060 came out around 1.5 years ago. If you don't want to spend much more than $300-$350 on a graphics card, at this point it might be worth waiting until after the next generation of cards launch. The high-end 30-series cards are expected to launch in a few months or so, and I would expect a more mid-range 3060 to launch a few months after that, bringing more performance to this price tier. Or perhaps AMD will have some compelling upgrade options available in this price range before the year is through.
As for the original question, power draw might not be a big concern. A 2060 only draws around 30-35 watts more than a 1660 Ti under load, and Nvidia recommends at least a 500 watt PSU for systems running this card. Being a pre-built, they probably don't put a high-end PSU in there, but what's there might be sufficient enough. Apparently HP sells some Omen systems with a 2060 running on their 500 watt PSU. Again though, it might be worth waiting for another card, as the performance upgrade wouldn't exactly be all that large.
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