Just tried to duplicate this, exported a text field "00123" (also without quotes).
The resulting CSV file had the leading zeros intact.
Therefore I assume you meant the zeros were lost when you linked to Google Docs.
This does happen, and can be fixed by formatting the relevant column in the Google spreadsheet as text.
Go to the spreadsheet, click on the letter (A, B, etc) above the column you want to format. This will select the whole column.
Click on "Format", then hover over "Number", which will raise a menu panel. At the bottom of the menu panel click on "Plain text".
This won't fix existing data, but subsequent syncs will retain leading zeros.