Cut-trough switching is not a standard. Actually it violates the 802.1D standard in some (minor) aspects.
So each vendor implement it on its own way and there's not a single answer to this question.
Beginning to forward the frame immediately after the destination mac address has been read doesn't prevent the switch to read the source mac while transmitting it, this could be a way to learn it with an optimal latency.
However most cut-trough switches will examine more than the single destination address field prior to decide to forward it.
In this article from Cisco you will find more information on this subject and more specificaly this paragraph :
Examining More Fields
Switches do not necessarily have cut-through
and store-and-forward "modes" of operation. As stated earlier,
cut-through switches usually receive a predetermined number of bytes,
depending on the type of packet coming in, before making a forwarding
The switch does not move from one mode to the other as
dictated by configuration, speed differential, congestion, or any
For example, in the case of a configuration that
permits or denies packets with certain IPv4 TCP port ranges, the
cut-through switch examines 54 bytes before it makes a forwarding
decision. For a non-IP packet, the switch may receive the first 16
bytes of the frame, if the user has configured some kind of QoS policy
based on the IP precedence bits in the type-of-service (ToS) byte or
on the differentiated services code point (DSCP) bits.
Figure 3 shows
a standard IPv4 packet structure in an Ethernet ARPA frame. The
cut-through switch takes in 54 bytes of the Ethernet header (not
counting the 8 bytes of the preamble, which serves only to wake up the
transceiver and indicate the arrival of a frame) and, depending on the
vendors' design, may then run a policy engine against the pertinent
fields in the IPv4 header to determine whether, for example, the TCP
destination port matches the ACL, or the source IP address is in the
range of that ACL.