Can Holo-Battle Interlink be played solo?

The AI teammates are the part that matters here. You are not dropped into an Interlink fight alone and left to cover every role yourself, so the mode stays available on your own schedule, without a queue or a group to organise first.

This is not special treatment for one mode. Battle Interlink modes in general can run with AI-controlled teammates, and Pathfinder challenge rematches use them as well. It fits the way the game is built: Aniimo has a single-player mode, and the majority of its content can be played entirely solo.

Egg Heist works on the same principle. Its PvE side can be played solo without a partner, or in co-op as a two-player team with a friend. The place where you genuinely need other people is PvP, the competitive battles players fight against each other in the floating sky metropolis. Those are real opponents, and no AI stands in for them.

Not settled: How AI teammates perform against a full group of players, and whether the fight adjusts when you bring them, is not settled yet.