If we seed c++11 mt19937 as the same on different machines, will we get the same sequence of random numbers

Inspired from this and the similar questions, I want to learn how does mt19937 pseudo-number generator in C++11 behaves, when in two separate machines, it is seeded with the same input.

In other words, say we have the following code;

std::mt19937 gen{ourSeed};
std::uniform_int_distribution<int> dest{0, 10000};
int randNumber = dist(gen);

If we try this code on different machines at different times, will we get the same sequence of randNumber values or a different sequence each time ?

And in either case, why this is the case ?

A further question:

Regardless of the seed, will this code generate randomly numbers infinitely ? I mean for example, if we use this block of code in a program that runs for months without stopping, will there be any problem in the generation of the number or in the uniformity of the numbers ?