Not sure what you mean by backup now that I re-read that. Are you meaning for it to run on a second set of batteries as a backup in case the set powering the MSW inverter goes dead? Kinda almost normall use type thing figuring the first inverter is the grid, and if that goes down then the UPS kicks to battery mode as normall.
To begin with I was thinking backup as refferring to a second inverter in case you fried the first one.

 It could possibly go either way depending on the 2 units connected. I have done various things like that and gotton mixed results. Sometimes a UPS works fine off one inverter but then connected to a different inverter it does not work at all.

In trying different things I have had cheap UPS of about 200watts just constantly click and clack switching from inverter power(grid?) to battery backup. But then connected to a different Inverter it would not even turn on at all and then connected to a third (really cheap small) inverter it worked fine.
 I actually ran that cheap 200watt UPS off a cheap 300watt inverter, but the expensive APC UPS (running on Batteries) and the Aims 5k inverter it would not run off of correctly.

I have had similar results in other combinations where one UPS will run on some inverters but not others. I tried alot of cominations. My largest UPS is a APC 1100VA and the smallest ones are those cheapo 200 and 350 watt ones like you buy at wal-mart, I also have some in between like a 600watt APC. My actuall inverters are a cheapo 300watt and a 5k Aims. Some combintions work and others don't!!

I would suggest if it's cheap enough go ahead and buy it and try it, if it doesn't work that way use it for something else or resell it later. Or if you can try it before you buy it and see if it works connected that way. It could just depend on your inverter, it might work on some but not others???
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nothing to lose

That is true.  Good UPS's for computers have 2 main tasks (1) keep supplying power when the mains is down and (2) always supply the computer with a clean, stable sinewave.

If it works as it should!
First His UPS should have fully charged batts. to start with, so if running from the other inverter it "SHOULD" just be a pass through, I see no real losses there. Maybe some minor loss in charging the internals to correct for self discharge, but I don't think that should be much. Now if something happens and the UPS is running off the batteries, then yes they will need to be recharged to full again and that will incurre losses, but then again that's the reason for redundancy is to keep things working, and they would not be working now if not for the UPS running on the Batteries.

Actually I think myself I would use each inverter as it's own inverter. Since your talking about the same power for each, then use the best one where you need it and the other for the other. Like if you have stuff in the house to make better use of the sinewave then I would use the UPS for the house and the MSW for the shop. Instead of only having 1500 watts of power total, you now have 3000watts total.

If you ran the house on the UPS and the UPS on the MSW inverter, then the house can still only draw the max the UPS can supply if the MSW goes off, and runing everything from the MSW there is a far greater chance of it going off due to over load.

As far as draining your batts. I think it's all still the same amount of power basically. If you still only use a total of 1500watts out of both inverters that's kinda cutting it in half 750watts each, will that increase the life of the inverters compared to running the full 1500 out of just one?

Now I would maybe run the UPS off the MSW inverter for things like computers where you really might want the backup protection incase of a problem like a blown fuse or overload shutdown or maybe the batteries go dead for the MSW for some reason. Something like that could scramble your hardrive just the same as a grid power failure, same thing right! SO for stuff that might need the saftey net I would do that. But really I think otherwise I would not. Just use the best for the house and the other for the shop.

Kinda what I plan to do, run the house off an inverter but then run a UPS also for the computers, then if my house goes dead I have time to safely shut down the computers after I save my work, then go fix the house power. Or if I have enough large UPS's I may just wire each to their own battery set to serve the same purpose, keep power to computers if the house goes dead. But I have 3 system here, and maybe 2 more soon, so that's alot of UPS's also. I would not worry about running computers off of UPS power as a pass through on a UPS and short time on batteries to shut them down in a failure, but I would not want to run them all off the same UPS on battery power all the time.

I geuss it's all a crap shoot how you look at it though.
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nothing to lose

I have a UPS somewhat like what you have/are thinking about buying which. While i "Could" run it off my 1500 watt vector inverter it would switch to/from BAtteries/AC every now and then.. i would suggest trying it out first...even if you have to drag the MSW there and run it off your car..