No. It is not okay to take Levoxyl and iron supplements together under any circumstance.
On the product insert, under "DRUG INTEREACTIONS:," it states to take levothyroxine (which what the brand Levoxyl is) 4 hours apart from iron supplements. The reason for the separation is that supplements can absorb the med before your body has a chance to, thus voiding its benefit. Food can do the same thing but the separation time on that only needs to be at least 1 hour.
Good luck.
Please contact your local pharmacist, they are very informative, in medication interactions.
I have read many mixed reviews on taking thyroid medications. But I would wait an hour or two, before taking a supplement. Until you get a definite answer from your doctor or a pharmacist.
Good luck to you !!