Definately,
First, create your custom fields from the Manage Fields page in the Freeform CP:
CP Home › Modules › Freeform › Manage Fields
(Click the Create a New Field button at the top right of page)
In your form, use something similar to the Freeform documentation:
{exp:freeform:form form_name="some_form_name" return="template_group/thankyou_template" required="name|email|checkbox1|checkbox2|checkbox3|checkbox4"}
<p>Name<br />
<input type="text" name="name" value="" />
</p>
<p>Email<br />
<input type="text" name="email" value="" />
</p>
<p>Checkbox 1:<br />
<input name="checkbox1" type="checkbox" value="Checkbox 1" />
</p>
<p>Checkbox 2:<br />
<input name="checkbox2" type="checkbox" value="Checkbox 2" />
</p>
<p>Checkbox 3:<br />
<input name="checkbox3" type="checkbox" value="Checkbox 3" />
</p>
<p>Checkbox 4:<br />
<input name="checkbox4" type="checkbox" value="Checkbox 4" />
</p>
<p>
<input type="submit" name="submit" value="submit" />
</p>
{/exp:freeform:form}
If you wanted the checkboxes to just be supplimental to ONE field, you could do it like this:
{exp:freeform:form form_name="some_form_name" return="template_group/thankyou_template" required="name|email|ONEcheckbox"}
<p>Name<br />
<input type="text" name="name" value="" />
</p>
<p>Email<br />
<input type="text" name="email" value="" />
</p>
<p>Checkbox 1:<br />
<input name="ONEcheckbox[]" type="checkbox" value="Checkbox 1" />
</p>
<p>Checkbox 2:<br />
<input name="ONEcheckbox[]" type="checkbox" value="Checkbox 2" />
</p>
<p>Checkbox 3:<br />
<input name="ONEcheckbox[]" type="checkbox" value="Checkbox 3" />
</p>
<p>Checkbox 4:<br />
<input name="ONEcheckbox[]" type="checkbox" value="Checkbox 4" />
</p>
<p>
<input type="submit" name="submit" value="submit" />
</p>
{/exp:freeform:form}
