Not soon, I doubt ever
Definetely not soon but chances are it will do it.
Transacting bitcoin is clumsy due to too low block size, and if they increase it, it only postpones the problem - not solve it (taking care of symptoms instead of curing the sickness).
Realistic time frame for Monero's takeover is somewhere around 2020-2025 area when the minimum block reward hits and the emission is dried out.
Then Monero will act like gold or silver and gain enourmous value (compare the marketcap of gold vs. marketcap of Monero).
Monero is adapted by new people as the Monero owners preach the good news and the new people will preach it even further.
In this way, Monero will be accepted as a currency of masses and if not as a currency, then a store of value to where people put their savings and watch its purchasing power growing with deflationary circumstances.
That's the best case scenario.
The worst case is, Monero will die and the investor loses the amount of money (s)he has invested into it. Nothing more, nothing less.
Also scenarios somewhere between can be realized but then I tend to think it is going to continue to the direction of goodness or badness and therefore the middle ground will not be a stable equilibrium.