Most generative theories of syntax insist that all branching must be binary, mostly for theoretical reasons: it's taken as an axiom that syntax trees are built using the Merge operation, which combines exactly two nodes, not three. But there are some cases where this assumption starts to break down.
This is not one of those cases. Constituency tests show that "in the room" is a constituent (a prepositional phrase).
It is possible but not necessary. Certain trends in syntax, following Kayne's Binary Branching Constraint, only allow binary branching, so as an axiom it is never absolutely necessary to have ternary branching (you just have to devise some binary structure). There are alternative theories, such as Simpler Syntax where, as you can see on p. 109 as a first example, "give Harry a book on Tuesday" has the branching (give) (Harry) (a book) (on Tuesday). In that theory, n-ary branching is necessary.