Can I charge a 12V battery with a variable, low-voltage generator?
You probably can.  

You would need a boost converter that can take an input voltage as low as the lowest voltage you expect from the fuel cell and make 12V (actually, you need over 13V to charge a nominal 12V battery) out of it.

In boosting the voltage, you will reduce the current.  The charge current for your battery will be lower than the current from the fuel cell by the same (ignoring losses) proportion as the voltage boost.  If you boost 1V to 10, you will only get 1/10 of the current at the higher voltage.

You have not provided enough information to even begin to guess how long it would take to charge the battery.

The time it takes to charge the battery depends on the capacity of the battery, and the amount of current you can supply.

If you have a 10 Ah battery, and a charge current of 1A, then it would take more than 10 hours to charge the battery.  It will take more time due to losses in the charging system and in the battery.

You need to find out how much current the fuel cell can supply, then divide that by the amount of voltage boost you need.  There you have your maximum charge current.  In reality, it will be lower.

Now, divide the battery capacity (measured in Ampere hours) by the charge current in Amperes.  The result is the minimum charge time you could hope for.  In reality, the charge time will be longer.  This number will at least let you see if what ever you are up to is workable.  If you need the battery charged in a hour and calculate 2, then it ain't gonna work.  If you calculate 1 hour, then you might be able to make it go in something close to your desired time.  If you calculate half an hour, then achieving the 1 hour charge should be fairly easy.  

The numbers you can calculate are just guides.  There's no practical way to figure it more closely without a lot more information about the fuel cell, the battery, and the charging circuitry that you probably don't have and can't easily get.



There is research going on in just this field.

Here is a link to a (fairly old) paper that discusses this very topic: DC/DC Converters for fuel cell applications.

Reading that should give you an idea of what you need to do to make use of your fuel cell.

If nothing else, you will find a bunch of key words to help you do better searches for more current documents.



Thinking about it, you probably want to look for a chip or premade booster that has the charge contoller for the battery built in.  

Lead acid batteries are charged using constant current switching to constant voltage at the end.

It would be more efficient if the boost circuit is operated so as to supply whatever is needed rather than converting to a fixed voltage and then doing CC or CV out of that.  You would have practically two converters, each with its own losses.

If anybody makes such a beast, it would on have one converter and so lower losses.



This converter from ST is an example of what you need.

It boosts the voltage and manages the charge, while also optimzing the load on the fuel cell so as to get the most power out of it - which will help shorten the charge time.

There are many such out there.  The example is only that, not an endorsement.  Given the lack of information in your question, nobody here can even guess if that part is adequate, or overkill, or too damn small.