Can a Vigenère cipher be solved if the alphabet is modified (custom)?
Basically, yes you can. To jump from alphabet to numbers without forgetting the + and / you can store the ASCII values in an array of 64 values.

Considering the order, it doesn't really matter as long as the cipher program and the decipher program use the same alphabet in the same order. You could use the ASCII order (symbol, numbers, uppercase, lowercase) or more probably the base64 order (uppercase,lowercase,number,symbol).

The list of the ascii values:

[43, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122]