Almost all New Testament scholars believe that the Pastoral epistles were written early in the second century. Bart D. Ehrman says, in Forged, page 99, the Jewish law is no longer an issue in the Pastorals, which of course include First Timothy. The last thing that would have been on the pseudonymous Paul's mind would have been the Jewish food laws.
On the other had, he could have had pagan food in mind, no doubt being aware that Paul had said in 1 Corinthians 10:27-32 that food sacrificed to idols would not harm Christians but that it ought to be avoided only in order not to confuse other Christians who may observe you:
If any of them that believe not bid you to a feast, and ye be disposed to go; whatsoever is set before you, eat, asking no question for conscience sake. But if any man say unto you, This is offered in sacrifice unto idols, eat not for his sake that shewed it, and for conscience sake: for the earth is the Lord's, and the fulness thereof: Conscience, I say, not thine own, but of the other: for why is my liberty judged of another man's conscience? For if I by grace be a partaker, why am I evil spoken of for that for which I give thanks? Whether therefore ye eat, or drink, or whatsoever ye do, do all to the glory of God. Give none offence, neither to the Jews, nor to the Gentiles, nor to the church of God:
Various other reasons have been proposed for the addition of Mark 16:18, but 1 Timothy 4:4-5 is not usually one of them.