Big YES for that but to know when, it is really hard to answer and nobody could tell neither.
Well, the adoption is in the process and continuous improvement. It can't be done so quickly depending on how the people/user will adapt to it. A lot of factors could affect this and one of these things is because of its volatility. Many establishments are still doubts and they are also afraid of losing their money once the market will dump.
I highly doubt that Bitcoin specifically can be a global payment solution alone because the only thing that bothers me nowadays to transact using Bitcoin is its fees. I still consider the time to be fair enough.
Recently I did search for alternate options to make transactions if the other party accepts or agrees on it. Tron is now one of my priorities to transact as its fees are quite less and the transaction completion speed is faster than Bitcoin as of now.
Hence, I don't know if Bitcoin will be able to make it acceptable as a global payment solution but I believe that surely atleast one crypto apart from BTC will be accepted globally.
I prefer Bitcoin as an asset now more than a mode of the transaction if I have the option.
And as you said volatility is another primary reason that can prevent this from happening.