If I have a motor performing on 2s with a certain prop.
Can I expect it to work on 1s with double the kv, same size motor.

What can I expect regarding current in 1s scenario?

Your post is a little confusing, but I'm assuming you have two different motors, one rated for 2S and one rated for 1S but the same KV value?

If you know the watts that each motor puts out you can figure the amps with this formula, amps=watts/volts.

In general though, if you lower the voltage in a system by half but need the same amount of power(watts), the current will double.

Of course there are other factors that affect this like how efficient the motor is, but that will get you an idea.

Sorry for being unclear.

Playing with a small tube build where i use a set of 1106 2700kv motors. They pull 0.5A on hover at 2S using 5030 props (quad is very light).

I wondered if I could move to a set of 1106 5400kv motors using 1S power drawing 1A getting the same lift.

What are the factors in play?

OK, now I get what you are doing. Sounds like you are trying to go as light as possible. Yes, you are correct that you should get the same amount of lift in that config. Sooo...factors at play?

Flight controller - does it function on 1S and down to voltage cutoff
Esc's - do they function on 1S and put out 1amp continuous
Battery - I'm guessing its pretty small so can it handle 1amp continuous

This is just my theory so bear with me as I have not tried or tested it with quads.

On paper, yes the end result may be the same amount of lift, but in the characteristics of real world flight I believe they will perform completely different with the same props, as one (the 2s) is high torque-low speed and the other (1s) will be low torque-high speed.

With the same prop, lets say an aggressive pitch, the torquey 2s will give a lot of punch/acceleration but lack in terms of top speed due to lower kv. Now that same aggressive prop on the 1s in theory should be twice as fast on the top end but lacking that immidiate punch that can saves you at times. The reality is that the low torque isn't going to be able to spin that aggressive prop at full speed putting more strain on the motors. 

If we step away from quads and into the niche of my 100mph Rustler. (2wd 1:10 scale RC truck) We find most people use high kv motors (4400kv+) and make just a couple high speed passes before, "oh no, my motor is blazing hot" (with a cooling fan) and have to let it cool down. Meanwhile I have mine built with a 2200kv motor and WAY over geared. (like over propping) I do just as many high speed passes and with better acceleration (it is more difficult throttle control)(just as with aggressive props) then while the high kv motors are cooling down Im still out bashing around for the full 30-40 minutes of my pack and never break 120-130 degrees. (with no cooling fans either) Guys have reached 160mph+ using the 2200kv setup and a 1:1 gear ratio. I reach almost 110mph with a ratio just over 6:1 in case anyone was wondering.

So in conclusion it may work, but you will definitely have to experiment with different props, and the flight characteristics will be completely different I believe.