We should still be trying to be realistic, and surely someone who starts today with accumulating $250 per week of bitcoin has a chance to reach 1 BTC in 10 years if they are able to increase their weekly (or otherwise) BTC purchase amounts in the coming 10 years. If they stay at $250 per week and have no other BTC purchases, they might not reach 1 bitcoin in 10 years...
This is true, anyone who started with this amount has a chance to reach 1 BTC in 10 years just like you said, but I think even if a guy did not increase his bitcoin purchase they may likely reach 1btc depending on how consistent they're towards thier accumulating journey, if they can't achieve thier investment target within this 10 Years they still have every right to extend thier accumulating journey to like 14 to 15 years or even more just so that they can be able to reach thier investment target, and sure this is all about determination once they're determined that this is what they want they will do everything possible just to ensure that they achieve thier investment goal.
Don't you think that the unit of Bitcoin he might be getting with $250 will decrease overtime?
Due to constant increase in the value of Bitcoin. I don't think it will be possible even if he stay consistent, what might makes him get to achieve that goal is if he can increase his discretionary income, and invest more, like $700-$800 per week, but with $250, it can't be achieved in that space of time even though the person is consistent, because the value of Bitcoin not waiting for you, it will keep on souring, so you get a smaller unit of it as time passes by.