Is "have yet to" a modal?

No, have yet to is not a modal. Your perception is correct, however, in that it has something in common with modals. The have yet to VP construction is a negative idiom, starring the negative polarity item yet. Like modals, negatives are Operators, which focus on one particular item in a sentence (normally it's the one that's stressed in speech; in writing it's not so simple).

A sentence like

• I have yet to see him.

is transformed from (and means the same as)

• I have not yet seen him.

Socially, have yet to Vinf falutes slightly higher than have not yet Vppt.
The latter is normal discourse, while the former is redolent of 19th-century prose.