I do agree with your statement and both goes hand in hand in my opinion. As the law of supply and demand goes, more demand means high prices of bitcoin. We already know that bitcoin has a fixed number only in circulation.
even if huge price increases didn't mean mass adoption,people still getting interested by its price rising and see this as some sort of worthy investment
Yes!both are important!if mass adoptation happens, bitcoins will become more indemand, many business establishment will accept bitcoins, and i yhink bank will also adopt bitcoins. The price will surely increase like on law of demand and supply, once the demand increase, the price will increase. so it is really possible that the huge increase of amount of bitcoins will surely follow.