I don't have thunderbird in a Windows environment. However on my system I can copy a table from Open Office into thunderbird, right clicking on the mail I'm composing gives me 3 options paste, paste without formatting and. pasted as quotation.
paste - pastes the gridded cells
paste without formatting - without the grid.
paste as quotation - same as without formatting but with a bar in front.
I'm using thunderbird 13.0.1
lubuntu LXDE 13.10 running on AMD Phenom II*4; ASUS Crosshair III Formula MB; 4 GB Ram.....