We have no problems with people adding ads to their own site, including AdSense. But keep in mind that:
- Your website needs to comply with AdSense’s program rules.
- AdSense checks website eligibility per domain name. Free subdomains are not evaluated separately, so you cannot get AdSense on a free subdomain.
- If AdSense will not let you use their service, that’s on them. Nobody here can magically get Google to approve your website. You need to sort that out with Google yourself.