Yes, this is permissible

Is it allowed to go home and do Ghusl( if the Masjid washroom are full or dirty) and have some food and come back during i‘tikaaf.

E'itikaaf | March 3, 2014 5:36 am
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When does one have to start i‘tikaaf on the 19th or 20th night of Ramadaan. What time does one enter into it?

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If a person starts his I’tikaaf does he have to leave it only when he sees the Moon of Eid?(For example if a person starts I’tikaaf on 22nd of Ramdaan he cannot leave until he sees the moon of the eid?