The first thing to note is that we will not burn all accessible fossil fuels, at least not within the next couple of hundred years, because to do so would be to pretty much destroy human civilisation. So one of the presuppositions in the question is incorrect.
And now to the effect of the rate of release.
Greenhouse gas concentrations are a stock problem, rather than a flow problem, at human timescales.
Think of a bath with one tap part open, running water; and with the plug out. The tap is open just enough that the rate of water entering (the source), is equal to the rate of water going down the plug hole (the sink). So the level of water in the bath stays the same. Turn the tap up a notch, and the bath will steadily fill until it overflows.
The problem with what we've been doing over the last two centuries, is that we've increased the rate at which greenhouse gases enter the atmosphere (source); and at the same time, we've been cutting back the Earth's capacity to sequester $CO_2$ in the form of soil and biomass (sinks). So greenhouse gas concentrations have been rising sharply.
And that means that climate is changing, much more rapidly than it would in the normal scheme of things. The Earth has warmed and cooled before. Over millennia, and over millions of years. Which means that previous climate change, has happened at the same sort of timescales that evolution operates, and so life adapts, over hundreds of generations.
When climate changes rapidly (massive meteor strike, anthropogenic climate change), then evolution doesn't get off the starting blocks, and we have a mass extinction (we're currently in what is, as far as we can tell, the Earth's sixth mass extinction event).
And having built much of our civilisation, our cities, and our food production, on the climate and sea levels we've had for the last few centuries, it's a real problem to change those things rapidly. So the problem, for life and for civilisation, is the rate of change.
And that's why the release time, matters. Higher emissions rates, mean faster increases in global temperatures, and much less time to adapt:
From IPCC AR4, on impacts and timescales: