Baha'u'llah did not meet Hazrat Inayat Khan as He passed away in 1892 in the Holy Land...and Hazrat Inayat Khan was then what five years old being born in 1887.
Apparently Hazrat Inayat Khan met Abdul-Baha in Paris around 1911 or so according to a search on google..
but as to Rumi.. there are quotes from well known Persian poets such as Hafiz, Saadi, Attar and Rumi scattered in the Writings of Baha'u'llah.. An example can be found in a book written by Abdul-Baha:
A story regarding Ustad Isma'il:
At one time, Bahá'u'lláh had written down an ode of Rumi's for him, and had told him to turn his face toward the Báb and sing the words, set to a melody. And so as he wandered through the long dark nights, Ustad would sing these lines:
I am lost, O Love, possessed and dazed,
Love's fool am I, in all the earth.
They call me first among the crazed,
Though I once came first for wit and worth.
O Love, who sellest me this wine, [1]
O Love, for whom I burn and bleed,
Love, for whom I cry and pine --
Thou the Piper, I the reed.
[1 This wine, Rumi says elsewhere, comes from the jar of "Yea verily." That is, it symbolizes the Primal Covenant established between God and man on the day of "Am I not your Lord?" On that day, the Creator summoned posterity out of the loins of Adam and said to the generations unborn, "Am I not your Lord?" Whereupon they answered, "Yea, verily, Thou art." Cf. Qur'án 7:171.] 31
If Thou wishest me to live,
Through me blow Thy holy breath.
The touch of Jesus Thou wilt give
To me, who've lain an age in death.
Thou, both End and Origin,
Thou without and Thou within --
From every eye Thou hidest well,
And yet in every eye dost dwell.
(Abdu'l-Baha, Memorials of the Faithful, p. 30)
Other than being regarded as an important poet and mystic though I don't know that Baha'is have any special deference for Rumi or other well known poets. Quoting these poets was quite common in the circles where Baha'u'llah could be found.
The Manifestations of God is a fairly unique Baha'i perspective and included Zoroaster, Moses, Jesus, Muhammad, the Bab and Baha'u'llah...
See:
The Eternal Quest for God: Chapter 6