Bethesda have confirmed that Fallout 76 mods will be available on private servers, but the mod support is likely not coming until November 2019. If this turns out to be the case, the game might be well on its way to dying off by that time.
Bethesda's official servers that will have up to 24 players will now seemingly be forever mod-free, with the official explanation being that the company doesn't want individuals coming with various mods that could be overpowered coming into public servers. Presumably, this modded content would be hard to balance out but more importantly, they wouldn't be able to sell cosmetics if modders just kept making new outfits for free.
There is no official confirmation for that second reason, but it's a quite obvious red flag for Bethesda. Either way, mods will eventually appear though, but only on private servers according to Pete Hines. We wouldn't recommend holding your breath though as the mod support will apparently not come before November 2019. Hines stated that "it's going to take a lot of work" but that Bethesda will eventually deliver mods and private servers in an interview with GameSpot.
Considering how much of the popularity Bethesda's games such as Fallout 3, New Vegas, Fallout 4 and Skyrim owe to mods and the modding community, it's hard to imagine that Fallout 76 manage to keep the players that interested for a year without them.
For example, Fallout: New Vegas is a solely singleplayer game that was released eight years ago that still manages to have around 3.000 concurrent players on Steam at any given time of the day. The Elder Scrolls: Skyrim is almost seven years old, also singleplayer and is averaging around 10.000 concurrent players every day, with the Special Edition having about just as many players.
Many games released in 2018 would kill for that many players, and these numbers have been fairly steady for over half a decade after Bethesda stopped officially supporting them. It is quite obvious that the modding community kept these games fresh enough, which eventually resulted in their longevity. It remains to be seen if Fallout 76 will manage to keep its player base for a year without the mods.