A complete CMaj11(#13) chord is spelled
C E G B D F A#, and a C11 (that is, Cdominant11) is spelled
C E G Bb D F.
So these are not equivalent, because one contains
B natural and the other does not.
However, it's true that both chords contain the enharmonically equivalent (i.e., they represent the same pitch)
Bb. The difference in spelling relates to technical/theoretical differences in how those pitches are used in context.
In jazz/pop contexts, chord spelling is often more a matter of convenience as ease of reading/understanding, but the underlying theory suggests that a
A#) should move upwards; whereas a
Bb) should move downwards.
As to whether the
#13 would be an avoid note against a
major7 chord -- more likely than not. It would be highly dissonant against the major seventh (
B), but could be quite useful in an appropriate musical context.
@JohnBelzaguy's comment on the OP is recommended reading. It explains how these chords are used (or not used, as the case may be) in practice.