Does a single LACP channel over multiple switches increase redundancy?
LACP itself doesn't provide the ability to bond across multiple switches; it bonds across multiple ports on a single ethernet switch, and depending on the vendor there might even be restrictions on which ports on a switch can be bonded together.
Some vendors have proprietary protocols (typically called MLAG) that allow for bonded ethernet channels across different ethernet switches. As an example Cisco Nexus vPC (or generically MLAG) works with switches, or bonding a single LACP port channel on a server across two connected switches.
Does the use of bonded ethernet channels across multiple switches (that we are advised that we can use) from the server, provide both improved throughput (unquestionably), and improved redundancy (uncertain). Could/would network events such as switch failure, port migration, patching, recovery, etc, cause the channel for both server network interfaces to be unavailable?
LACP should provide protection against a single physical port or cable failure within the LACP channel.
LACP cannot protect against human factors, such as accidentally shutting down the LACP-interface, removing the vlan, or running a TDR on a port-channel member link. LACP also cannot protect against over-provisioning bandwidth through a single member link on that LACP channel, spanning-tree events, broadcast storms, excessive unknown unicast flooding, etc...
If you are concerned about recovery time, be sure to use short LACP protocol timeouts on your interfaces.
LACP can usually only be accomplished to a single device or group of device that act as one. So... you could do it between a switch and a switch stack, but not spread out across multiple unique devices.
LACP is a protocol for the host to communicate to the switch(es) that it wants to aggregate multiple physical connections. This aggregation might not always be possible however. If the connection is made to multiple switches those switches must support some method of cooperating to make the bonded link or they will be unable to.
Most switches do not support this cooperation. Some however do. The most common method is the SMLT protocol, which allows switches to cooperate in creating bonded links. Some switches also support stacking protocols that enable multiple switches to act as a single logical switch. In either case you'll want to check the documentation to be sure of support and configuration.