Who has that assumption? At some point ads just reach steady state as a percentage of an economic sector, and therefore their growth simply mirrors GDP growth. Yes it will grow forever as the economy grows forever, but no faster.
I don't think anybody thinks advertising is going to eat the whole economy, so I don't think there are any implications in that not happening.
Economic growth might not stop in next 10 or 100 years, but natural limits exist and eventually growth will stop.
You can get 5% GDP growth without any actual growth by just devaluing dollars by 5% more than you measure inflation.
Theoretically, there's nothing stopping people from paying more money for monkey JPEGs indefinitely.
Physically, there's limits to how efficient things can get.
To the contrary, if you figure out a way to manufacture the same widget X but using 25% less energy, that's economic growth.
Long-term economic growth is primarily a phenomenon of increasing human efficiency which is enabled mainly via improved education which leads to ongoing technological progress.
Sure we need energy to heat our homes and grow our food and power our transportation and build our phones and so forth, but those needs are not growing exponentially whatsoever. Homes in the developed world, for example, are becoming more energy efficient rather than less.