It depends on what you mean by free roam, because it can mean very different things.
It also depends on the rest of the game: if the game is mainly a linear VN, it may be better to stay consistent and do the same for the part with the side characters, or just add a menu where the player can choose which characters to talk to, as some games do.
But developing relationships with certain characters outside the story can be a good idea in my opinion.
Something simple like Mass Effect for example: you have a set of characters, you can take some of them on missions and leave the others at the base. Most of them can be considered main characters, but I think the same reasoning can be applied.
When a mission ends, you can chill in your base and go talk to everyone (or no one). Each time you talk to a character, they'll tell you part of their story.
Then you go back to do a main mission, and when you come back and talk to him again, he continues his story and so on, until you know the character well enough for the relationship to progress.
I don't think it's a bad design.
Now if you don't want the player to feel forced, you can, for example:
- not make every interaction mandatory: a player doesn't have to talk to every character every time.
If he misses a few opportunities and goes back to talk to the character later, he'll "catch up" with that character's story.
And you can also show a warning (or something more subtle) at some point to let the player know that if they continue to ignore a particular character, their relationship with them will not progress anymore (if you need the relationship with this character to have progressed sufficiently in order add a scene in the main story, for example)
- You can also make these dialogues totally optional (and warn the player that they are): the player will still be able to progress the relationship with the character even if he doesn't talk to them. Talking to them might only give a small bonus to the player which facilitates the relationship, so if a player doesn't want to do that, they could simply skip these dialogues. It could be, for example, a direct benefit, such as a bonus scene with this character, or something more indirect, such as an element from the character's past, which the player has learned from these optional events and which he can then reuse later in the story to resolve a particular situation.