Yes, we have seen LabVIEW running on an ARM7 running eCos as an operating system. There's no reason that it shouldn't be able to run in other configurations as well. As is the case with any LabVIEW Embedded Development Module target, however, this will require some up front integration work by you in order add support for the target to LabVIEW.
It's not critical that there be 256K of RAM for the applications to execute, however, you will need at least 256K of program space (this can be RAM or FLASH ) in addition ot whatever is necessary for your OS or support libraries to have enough room to develop a reasonable LabVIEW Embedded application.
For more information on what is necessary to bring up a target, you can check out the training class for LabVIEW Embedded here.