Can a message be encrypted with BOTH mono-alpha and poly-alpha ciphers?
I'm assuming that your Columnar Transposition Cipher (CTC) is as described as this site, since I found that the keyword ANNIE works.

OTP

First of all, the combined cipher (Caesar shift 7 plus CTC) can always be the OTP, as long as we don't require a truly random OTP. The simple reason; x-or the plaintext and ciphertext get the OTP keystream.

This is your OTP key;


  zpgzmdgvimgddgwmfdypurgdaagcgqhhulnohospvisfikencaiuspaplrpvdszgpjctgigfzmlrtuordrxzuzttzyllcyuvcdmzbsvnorznadqieerdcneslflvnqztpknyohgagorodtazczrdypyshyrolzigrnvtxaceufmrjusmyvtichxpdxsttpsousllyccusveqhodrnpfzrzuubmtjyvqag


And if you asked if OTP can replace the CTC, the answer yes again with the key;


  sizsfwzobfzwwzpfywrinkzwttzvzjaaneghahlioblybdxgvtbnlitiekiowlszicvmzbzysfekmnhkwkqsnsmmsreevrnovwfsuloghksgtwjbxxkwvgxleyeogjsmidgrhaztzhkhwmtsvskwrirlarkhesbzkgomqtvxnyfkcnlfrombvaqiwqlmmilhnleervvnloxjahwkgiysksnnufmcrojtz


Vigenère

In the Vigenère cipher, the password only affects $\operatorname{StrLen}(\text{password})$ characters whereas the CTC distributes the plaintexts implies they are not equal ciphers.

Note: If Vigenère is equal to CTC then the security will be the same as CTC.

Note: there may be a collision that is for some plaintexts a Vigenère Cipher will produce the same ciphertext as a CTC. This will have very low probability, and generating one is an interesting question.