Yes, eCart can do this.
for each form field you are going to create, you need to add a column in the eCart object. When adding the new column for the product options, you will need to check the Unique box for each option column.
then in the add to cart button, on the bindings panel, select each option column and set it to be editable from a text box.
after the add to cart button is set up, you can change the text boxes to check boxes in the code by changing the type attribute to type="checkbox".
When using checkboxes, make sure to set a checked value.