Yes it is... Before that your need add Generic property field on related document type, and then go to this javascript file "teacommerce_simple.js" to this method "sendCustomerInformation" and add another property in "formObj"

 var formObj = {

    company: paymentInformation.find("#company").val(),

    firstName: paymentInformation.find("#firstName").val(),

    lastName: paymentInformation.find("#lastName").val(),

    city: paymentInformation.find("#city").val(),

    zipCode: paymentInformation.find("#zipCode").val(),

    streetAddress: paymentInformation.find("#streetAddress").val(),

    phone: paymentInformation.find("#phone").val(),

    email: paymentInformation.find("#email").val(),

    comments: jQuery("#comments").val(),

    shipping_firstName: shippingInformation.find("#shippingFirstName").val(),

    shipping_lastName: shippingInformation.find("#shippingLastName").val(),

    shipping_streetAddress: shippingInformation.find("#shippingStreetAddress").val(),

    shipping_zipCode: shippingInformation.find("#shippingZipCode").val(),

    shipping_city: shippingInformation.find("#shippingCity").val(),

    Your Property: filed value

  };

Then it should work... :)