Establishing a physically enforced unidirectional Ethernet link with 1000BASE-X, fiber optic PHY
Receive synchronization should not be required to transmit data.  However, in some cases the transmit chain is disabled at some point if there is no signal on the receive side.  What are you putting the transceiver in?  NIC?  Switch?  Custom device of some sort?  I have some experience with running SFP+ modules unidirectionally for various photonics experiments.  Generally, the SFP+ module and PHY are no problem, it's at the MAC layer or higher that you can get trouble if there is no receive signal.  The technique I used with standard 10G NICs was to loop the transmit side back to the receive side of the same module with an optical tap, either a 90/10 tap or I think a 98/2 tap.  With driver modifications to mask the link status from the operating system, it was generally possible to run without the loopback, at least for the specific NIC that we were using.  I presume this should work for your application as well.  However, if you have control over the MAC higher layers and you can configure them to ignore the receive side status, then this may not be required.  I have had no issues with running SFP+ modules transmit-only with no receive connection out of an FPGA board.  

You may just need to do some experimenting; gigabit NICs and SFP transceivers are rather cheap second-hand.