Yes, that would work, in theory, but its hard to dye over red depending how red and how dark. I tried to do it myself about a year ago and it got darker but the red shines through. If you add more colour to hide the red then you get colour build up and then when you want to go light, you can't get the lift you need from the bleach and your highlights will be orange, giving you an even warmer redder overall look!
Therefore the best thing to do is to get rid of as much colour as possible using ColourB4 Extra Strength. It will melt away a lot of the artificial colour (its not bleach, it may dry you out a little but its only drying you not stripping out proteins or changing the structure of your hair).
You will go ginger. You can put an ashy or just brown temporary colour over the top (no ammonia or peroxide) to cover the ginger a bit. But you have to wait a week before you do a permenant dye as the colour can reoxidise otherwise. This is less of a problem with reds as it is with browns and blacks - reds are easy enough to rinse out, the molecules are already smaller, though they can leave behind some cuticle staining.
Anyway, do the ColourB4, check my profile, as there are pictures of me after I got rid of my reds (looking pretty pinky ginger) and then a picture of me after I dyed it using Nice n Easy 114 Light Ash Brown. The ash kills out the ginger tones and leaves you with a natural looking light brown shade. This is the ideal base from which to go blonde again. I know because that's what I then did - though I don't have any photos of me blonde on there. So I'd recommend you use that shade when you are allowed to dye it again.
So basically when you feel ready to go blonde again, go to the hairdresser and get a full head of highlights. She should be able to bring you up to a good level of blonde as you will have no colour build up, just the hair stripped of its reds with one layer of permenant dye as a toner. Then you can gradually get more and more highlights as your hair recovers and become blonde.
If your hair is in really bad condition, consider doing the Keratin treatment at home on yourself - mine was fairly overprocessed recently and all the oil treatments were not doing anything - but I did the keratin treatment and now its soft and bouncy. It puts protein back into your hair in the way other treatments can't - it actually bonds to the existing proteins in your hair. This
Good luck, let me know if you have any questions