I think the title is a bit weird, rather skewed towards a different scenario than the one discussed in text. Reading it, I was first thinking at Mars, where because of the loss of its internal geomagnetic field, water sank out to space. But your text only refers to evaporation, which is one part of the present-day oceanic-atmospheric cycle of water, the other being rain.
On Earth, there is another water cycle with a much much longer timescale, which is an interior-surface cycle. Four cycles in fact :
- water in sediments and altered oceanic crust returns back to the mantle, some of which goes along within the internal convection, and then mostly outgases at ridges, and
- some of which takes the short circuit of subduction zones (much more intense, but shorter term). The quantity numbers of these fluxes are still much in debate, but there is a big lot of assumption but the amount of water inside the mantle is larger than what is present at Earth surface, with a range from an equivalent amount up to sort-of five times (not an order of magnitude more, but rather a significant amount).
In terms of characteristics duration, the subduction cycle takes a few tens of million years, while the cycling through the upper mantle convection is in orders of a very few (one to three ?) half-billion years.
- There is a deeper cycle, supposedly much longer, which comes from the potential reinjection of hydrated material down to the core-mantle boundary ("CMB"), the so-called D'' layered zone (pronounced "dee-double-prime") ; it's a thin "layer" laying at CMB, not thicker than 100 km, heterogenous in properties, accumulating some of the oceanic slabs material that might have come down though the whole mantle (about 3000 km thick !), not detected to be present all around the core, and it is the origin from which big hot plumes rise, as seems to be the case for Hawaii hotspot. As far as water is concerned, the effectiveness of this very deep cycling process is still in debate.
- Finally, it seems that there still exists some pristine material inside the lower mantle (between 570 km and the CMB, accreted at time of Earth formation, and which still has kept it primary load of volatiles (shortly said : geochemical observation of xenon isotopic anomalies in Loihi seamount lava). Therefore not a cycle, but a proper source, a spring !
These last two very deep potential sources for water, either pristine or recycled, would have characteristics durations in orders of magnitude of some billion years…
Therefore, the discussion of water cycles and water exchanges between internal Earth reservoirs and the atmosphere-hydrospere, at geological time scales, say durations between the one million years beat up to the four and a half billion years of Earth being, is quite different than the one for the meteorological and climatic cycles. No need to say that drying this Earth, its interior the mantle, will last much longer than will humanity :-).
This to say that the comparison of the hydrated fate of the Earth interior, with some well documented past situations of the surface Earth (recorded as the geological history of climate, no longer than, being large, a pair of hundredth million years), is not that simple.
And for the Venus case, whom so little is known except that it does not seem to house a large-scale internal convection, rather "only" a plume/hot-spot one…, we still lack many fondamental informations.
In conclusion, drying up the Earth (as in the title question) is a totally different question to that of evaporating the oceans (as in the question content).