First up, uploading MIBs won't make any difference. MIBs provide mappings between numerical OIDs and textual representations, but they don't in themselves change any monitoring or management behaviour in IMC.
Backups are done via a variety of methods. SNMP read-write is used by some devices - IMC will send a SNMPset, and the device will upload its configuration via TFTP or FTP. That can work for devices like Cisco switches, assuming they have SNMP read-write configured.
But many devices don't support that method (or more generally, don't support SNMP read-write). That's why IMC also uses other methods, such as Telnet, SSH, SCP, SFTP to get device configs.
IMC uses Device Adapters to configure the backup methods. MIBS play no part in any of this. Chapter 6 in the Admin Guide goes into more detail on the adapters, and how to create them.
Backup support is configured by HP on a per-device basis. They only enable it for devices they have tested. Sometimes newer devices come out, and they appear to be different to IMC (they have a different SNMP sysObjectID). But since IMC already supports other similar devices, we know that the backup process should work.
Cisco ASAs are already supported, and same with some other models of SRX. You'll need to edit the Device Adapter to add the new sysOIDs, restart IMC, and re-synchronise the devices. Here's some notes on doing it for Cisco switches - the process will be very similar for the ASA and the SRX: http://lkhill.com/help-imc-doesnt-support-my-new-cisco-switch/
There are some other modifications and custom adapters available here: https://github.com/NetOpsCommunity/imc-netops/tree/master/adapters/ICC - that includes changes to the Juniper adapter to include support for a couple of other SRX models.
You'll need to develop your own adapter for the BlueCoat system. If it has a CLI interface similar to say Cisco, then it's usually not that difficult to write your own adapter.
You'll need to develop