Hi benj5,
Cannot find anything conclusive but I would not expect it to be supported when looking at the following:
1. SRX-MP-1SFP-GE is only listed as an accessory for SRX550 and SRX650 in the official price list.
2. Not able to add a SRX-MP-1SFP-GE mPIM module to a SRX340 in the official Juniper configuration tool. On the VDSL, serial or the T1/E1 module.
3. SRX-MP-1SFP-GE is not mentioned in the SRX300 series datasheet.
and as the last thought: Why at all use the SFP mPIM on a SRX340 which has 8 built-in SFP ports?
My guess is that the support was not properly removed from the Junos codebase and never tested what would happen if a module was inserted.
Best suggestion: Use one of the built-in ports instead :-)