Yes it is doable.
Calculate your cumulative usage (since your bills started) for each gas bill. Interpolate the cumulative usage for the 1st of each month. For Feb 2007 = (Mar_1_2007_cumulative - Feb_1_2007_cumulative).
Goal "... consumption over time - kWh by calendar month."
Even if you had daily consumption figures, as months like January (31 days) are longer than February (28/29), charting what you request would show a + bias in long months and - bias in short months. So let's change the goal to
Goal "... daily consumption over time - kWh/day by calendar month."
Say you have figures like where you list the data, usage since last data and you calculate the cumulative usage since the beginning of your records set.
date kWH *1 Total*2
Jan 1, 2012 - 0
Mar 3, 2012 100 100
Apr 4, 2012 30 130
May 2, 2012 35 165
Aug 9, 2012 75 240
Dec 25, 2012 100 340
Jun 7, 2013 200 540
*1 energy used since previous period
*2 Sum of total usage
(Ignore the "kWH *1" column for the following)
Now make a table for the first of the month for a year, say 2012, and find in the above table an entry <= the first of the month, and the next entry.
Jan 1, 2012 (Jan 1, 2012 0) (Mar 3, 2012 100)
Feb 1, 2012 (Jan 1, 2012 0) (Mar 3, 2012 100)
Mar 1, 2012 (Jan 1, 2012 0) (Mar 3, 2012 100)
Apr 1, 2012 (Mar 3, 2012 100) (Apr 4, 2012 130)
May 1, 2012 (Apr 4, 2012 130) (May 2, 2012 165)
...
Dec 1, 2012 ....
As dates can have a serial number, you liner interpolate that serial number into the the 2 date/cumulative_usage pairs. this provides the cumulation usage to your 1st of the month. That becomes column "Interpolation" for the below table. The "Days/Month" is straight forward (days form First of the month to the next). The Usage/Day for a given month is then the (change in "Interpolation") / "Days/Month". E. g. 1-Feb-12 --> (96.8-50.0)/29 = 3.34.
Date Interpolation Days/Month Usage/Day
1-Jan-12 - 31 1.61
1-Feb-12 50.0 29 3.34
1-Mar-12 96.8 31 4.10
1-Apr-12 127.2 30 5.46
1-May-12 163.8 31
All thats left is to chart Usage/Day vs. Date.