Often, the spaces can indicate a tongue positioning issue and can be associated with airway problems in later years. Closing the spaces CAN create a problem. Similar to a person that drives a Cadillac and has a garage that fits a Pinto. If your tongue wants space, it needs that space.
You may want to consider porcelain veneers. Similar to your bonding, it can close the spaces but still leave room for your "Cadillac". If done well, they will be smooth and will not catch floss as your current bonding does. Veneers will allow the teeth to be the right size (you state that they are too small) and can be whatever color you desire.
The answer to your question is yes, Invisalign can work. Traditional braces should be considered as well, but a comprehensive exam should be done to rule out other issues.
