Is it possible to use the principle of EHT to build a virtual gravitational wave detector to detect very long wavelength gravitational waves? The press conference of the EHT is fascinating. While there are some features such as the asymmetry in the ring that is to be followed up by the team, I was actually wondering, whether it is possible to have multiple LIGO detectors scattered on the planet and in orbit in the future so as to create a virtual gravitational wave detector the size of our planet in order to detect and measure e.g. $10^{10}$ year period waves that are relevant to the primordial large scale structures of the universe?
 A: It's actually already the case that there are multiple "LIGO" detectors scattered across the earth.  LIGO itself has two detectors — one in Washington state and another in Louisiana.  There is also the Virgo detector in Italy.  By combining the measurements from these three detectors, gravitational-wave (GW) astronomers have been able to improve their ability to pinpoint the sources of GW events.  Most importantly, all three detectors provided information that helped pinpoint the event GW170817, which let electromagnetic astronomers view the same event for the first time.  There are more GW detectors that should be coming on line in the coming years in India and Japan, which should further improve our ability to pinpoint exactly where these signals are coming from.
And this is also the crux of what EHT does: it improves angular resolution.  But it does not enable measurement of different frequencies.  So a larger GW network will be measuring the same frequency ranges that any single GW detector will measure.
More generally, it will be hard for humans to ever directly measure anything that varies over a time period of anything like $10^{10}$ years — basically because you need to actually make your measurements over at least a significant portion of the period to be able to conclude that something is oscillating.  And since a human lifespan is only ~100 years, and human civilization has only existed for ~5000 years, we can't directly measure periods much longer than those.  Of course, it is possible to look at traces left behind by long-period oscillations over some region of space.  And to a certain extent, that's the goal of space-based GW telescope (LISA and its successors) — to probe cosmology.  But as for direct measurement of $10^{10}$-year oscillations, the answer is no: that's not going to happen in our lifetimes.
A: Very long baseline interferometry is based on measuring both the intensities and the phases of the incoming signals and then being able to resolve the position of the signals on the sky better thanks to comparing the phase differences. It does not change the wavelengths you observe on, all the nodes must be able on the same same wavelength even individually.
In this sense of the word, the LIGO/Virgo network is already using very-long-baseline interferometry. However, they have an extremely small number of nodes (3) and none of them provide directional information! A single-node network would thus ascribe a single pixel to the entire sky, and you get more and more pixels as you add more detectors. Once again, all the detectors must observe on the same frequencies ($\sim$ kHz) for LIGO/Virgo, interferometry will not be able to change that.
There are projects that want to extend to other frequencies/wavelength. The space-borne detector LISA is planned to observe $\sim$ mHz gravitational waves, and there might be some cosmologically interesting signals in that band (note that the LISA arm length, 25 million killometers, will be way larger than the Earth). However, the greatest promise for coherent old cosmological sources of gravitational-wave observations is the Pulsar Timing Array, that should be able to detect in the $\sim$ nHz regime. In a loose sense of the word, you can understand the Pulsar Timing Array and the way it will be used as a gigantic interferometer-type device.
