I am wondering why, since the oceans could feasibly hold all of the dry land, they in fact do not. For example, the Mariana Trench drops to -10.9km, while Mount Everest only reaches to +8.8km. Further, the oceans cover 71% of the surface. This causes me to suspect that the negative elevation parts of the Earth could easily hold the positive. Due to erosion, will the oceans eventually consume the mountains? What is the timescale involved with such a process, and what forces counteract it?
If no new mountains were built, yes. Ultimately the processes of erosion would render the continents flat, and the seas would be left shallow and filled with sediments. The reason that this doesn't occur is that tectonic processes cause 'orogenesis', the formation of new mountains. The subduction of oceanic crust at plate margins is also responsible for trenches such as the Mariana, and ultimately recycles sediments into the mantle; thereby preventing the ocean floor from filling up.
As long as plate tectonics persists, then, as @Arkenstein mentions, mountain building and ocean basin formation will create enough topographical variety to ensure that land exists. Moreover, as long as there is a distinction between continental and oceanic lithosphere, we will have continents.
But this will not last forever. At some point, plate tectonics will stop as Earth's internal heat production falls. At this point, assuming nothing else happened, we would gradually see the mountains erode, and the sea fill up - slightly - with sediment. Erosion stops at sea level, give or take, but sea level itself changes over time, so you might expect a world of very shallow seas where the continents used to be.
But that isn't the only thing going on.
If plate tectonics stops, we would likely move to a Mars-style regime, with hotspots being the dominant mode of heat transport. And as with Mars, we would see huge shield volcanoes form, basically like Iceland. So imagine an ocean planet with some massive circular islands dotted about, as the old continents eroded down.
Of course, this won't actually happen; within about a billion years, the sun will get so hot that a runaway greenhouse effect will come into operation, and the oceans will evaporate, ending pretty much all life on earth, and the possibility of a global ocean. Indeed, with no mountains to draw down CO2 by erosion, a water world may be very unstable as regards runaway greenhouse effects.
Note that you may have a bit of a misconception: the land heights/ocean depths, even what % of Earth is ocean, aren't too important because when land erodes, it doesn't fill in much of the depths, but instead raises the ocean bottom AND ocean top by similar amounts - the amount of water on Earth still needs somewhere to go! It still just tends to sit on top of the land. If you took a cup half filled with water, then dumped sand into the water, it doesn't take up all the water depth, but instead raises the water up in the cup:
The related question If the Earth were a smoothed spheroid, how deep would the ocean be? discusses how deep the oceans would be if the Earth became perfectly smoothed out and there were no change in the amount of mud (the question is, would the old sea bottom, now buried beneath the new dirt, then gradually lose some of its water? I think the answer would be yes, but it's still true that a bit of the water may be permanently tied up into additional mud).
Erosion is indeed the process that would tend to smooth out the ground level. However, anything that causes uneven vertical movement in the ground would work to counteract that. Plate tectonics like mountain building and sinking plates would do so.
So I think the answer is clear that in a tectonically inactive Earth... if the Earth kept enough water during the process, we would eventually have an ocean-covered planet.
But on the other hand I'd suspect for a 4.54 billion year old planet, if it weren't for tectonics, the Earth would probably already be long since smoothed out. So it comes down to whether plate tectonics will slow down/change in the long run, which geologists can likely better discuss (and which may be a good separate question to ask). But either way, there will be some important uncertainties [large meteor impacts, global temperatures changes, etc]
So I'd think the best answer may probably just be: not anytime soon!