Can we see Base64 with this new table as some sort of [..] encryption [...]?
Yes, technically it does constitute a form of encryption as knowledge of a secret key is required to recover plaintext from ciphertext.
Can we see Base64 with this new table as some sort of safe encryption [...]?
NO! This is essentially a monoalphabetic substitution cipher applied on the Base64 encoded data. This can be seen as you can always take your table $T$ and then find a new $T'$ that undoes the base64 table encoding first and then applied after standard Base64 encoding.
Now while the key size is (theoretically) respectable with $\log_2 (64!)\approx 296$ bit, this cipher suffers from all the usual problems such ciphers have, including:
- Ciphertext-only attacks are possible using frequency analysis, as there are only 64 valid plaintext values and they will probably occur with different frequencies.
- Known- and chosen plaintext attacks are devastating as there are only 64 mappings to be uncovered and usually plaintexts have quite a bit of structure allowing to guess the rest / uncover significant parts of the plaintext.