That’s a good question to investigate.
According to VESA.org:
While eDP 1.4b represents the latest VESA Embedded DisplayPort standard, systems in production today are using displays built to eDP 1.3 and earlier. By mid-2016, systems will begin to incorporate eDP 1.4b, and the final standard should continue to increase in adoption and be used in production for several years. In the meantime, VESA members will begin discussing plans for eDP 1.5, which will take advantage of new features that will be introduced in the future release of DisplayPort 1.4. The eDP 1.4b standard is available to VESA members. More information is available at www.vesa.org.
Another hint that it might be possible is this cable, which proports to enable an eDP connector to plug in with a Display Port cable (you might need an external power source to make this work). Since DisplayPort is designed to be backwards compatible, it stands to reason that the eDP equivalent could work.
According to EETimes India:
The ongoing enhancements to eDP v1.4b have been made possible by the flexible nature of DisplayPort. DisplayPort [note: NOT eDP - Soda] is highly extensible and includes the ability to remain backward compatible. An extensive register set is implemented in the sink (display) device to support both new and old features, and other registers indicate device status and allow control by the source. Data packets in the high-speed video interface include pixel data and other various control data. The VESA member companies developing the eDP ecosystem have added the special features described in this article using these DisplayPort features. This will continue, and there is already discussion about a future eDP v1.5 that will utilize the features of DisplayPort v1.4, recently published in February 2016.
This paragraph suggests that eDP 1.4 incorporates backwards compatibility as a feature of DisplayPort (do not confuse DisplayPort with eDP - they are different but similar). So agian, nothing is certain, but it’s possible.
It’s not very explicit, but it seems to suggest that 1.3 displays would work on 1.4 hardware. You’d be on your own to learn about how much this applies to this particular use-case, but theoretically the main difference in 1.4 is power savings, and it should otherwise be pin and protocol compatible.
Frankly, I think it makes sense for it to be compatible with 1.3. Remember: a lot of transition happens, but a good standard is one that enables the least rework by the stakeholders, and someone who runs a computer fab won’t want to redo everything all at once. Supply chains are already complicated, and adding to that complexity is not an attractive position for anybody involved. On the other hand, there was an eDP standard that was said to have eliminated some pins, I can’t find information indicating whether these were eliminated from the physical connector itself. In either case, you might take a battery life hit, since the 1.4 standard explicitly added power saving features.
So experiment with caution, knowing that you might not get what you’re hoping in exchange for money spent. This is an experimental situation, but it could also end up in your favour if it does work out.