Mostly yes.
There are other things that might factor into it, but mostly the questions of how many bits per second can be moved between the server and your device, determines how long it takes until all the bits that make up the game end up on your console.
Most of the time the problem is with the bandwidth which with you connect to the internet as a whole, because that is the weakest link in the chain, but in theory bandwidth constraints at any other point in the connection might be responsible.
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