Not sure about those specific places, but it could be complicated. Boulder has a great network of paths. I saw a map once that showed that some of them allowed ebikes and some did not. The ebike-allowed paths seemed to be random and were not connected. You couldn't really get around using them. I doubt many people, including police, know the rules.
If you ride responsibly, I would guess you'd be fine. Ebikes are fairly common. Keep in mind that the rec paths are probably not "bike paths", but rather "multi-use paths". They are full of walkers, joggers, longboarders, baby carriages, homeless people sprawled out, dogs on and off leash, fishermen, geese, prairie dogs, and raccoons. Half the people have headphones and won't hear you coming even if you announce yourself. Some are on the phone waving their arms talking with their hands. Some are high. It's hard enough not to hit them with a regular bike.