I do not think so. Based on your readings your FC is too low. You should add chlorine manually and you probably need to add CYA. Click on the "Pool School" button on the home page. There is a lot if good information there.
Others will post with better info than I am providing you now, but if you are in a rush to get started then you need chlorine in there immediately. If you want to keep it simple, you could add the bleach now and then add the chlorine that looks like white hockey pucks (dichlor, I think). That will add chlorine and CYA. I would continue with that until the SWG keeps you FC between 3.0 and 5.0.
Adding chlorine in any form when you have metals in the water will cause discoloration - sometimes yellow, brown or greenish blue. However, if you have metals and have used appropriate amounts of sequesterant will not cause the discoloration - NOT having them will.
You need to get your CYA up there to an appropriate amount for a SWG pool (usually around 70) and your FC at about 2-4ppm. I'm thinking your PH may be hanging right on the edge of low - perhaps watch that, but since SWG usually result in PH drifting upwards you may be OK - just keeping an eye on it. Now, you can start off with some pucks or bags of the pool store powders (not Cal Hypo - no CYA there) if that is all you have around but the best route is the granular CYA in a sock in front of the skimmer and bleach. People with pucks and powders feel like they are obligated to use them since they paid for them and often don't carefully watch the CYA levels - which can take up to a week to register, depending on different conditions so by the time they know what they have - it can be too late and only fixable by draining. Carefully measuring amounts for your pool volume is really the best way to get what you need and be confident that you are where you need to be.