At least Django template language is quite silly - the logic should not take place in the template - so think about a template tag => register your own and try to move the logic in the view...
In this case the question might be why you're trying to do this?
Probably it might be easier to use the variable directly where you need to and in case it is None use the default template tag / function:
{{ product.url|default_if_none:default }}
But anyway your solution might look like:
{% with a=default %}
{% if product.url %}
{% update_variable product.url as a %}
{% endif %}
{% endwith %}
And your template tag should look like:
@register.simple_tag
def update_variable(value):
return value