The question may well depend on the state that the property is located in, so you need to consider directing this question to an attorney in the state where the property is located.
In general, the issue would likely be less of whether you can rent out the property and more about what happens if the person redeems within the period. If the tenant is thrown out of the property by the prior owner who redeems, you may well face liability for signing a contract saying that you are giving the tenant possession and that you have authority to do so for the full period of the lease.
Again, while you need to talk to an attorney in the state where the property is located, an option may be to do a month to month lease to a tenant during the redemption period while fully disclosing the situation. It may well cause you to get less rent, but it may help you avoid the risk of not just losing rent but owing a potential tenant damages if the property is redeemed.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. I am licensed in Arizona and can only provide general comments on matters outside of Arizona law. Actual legal advice can only be provided after a direct consultation in which all of the relevant facts are considered before providing a response.
In Georgia the purchase of a tax lien does obligate you to payment of HOA assessments jointly with the title holder, but does not grant you full title or ownership rights, as those are subject to redemption. Therfore, the purchase doen't allow you access to the property during the redemption period. Claiming full ownership rights of the property, especially if the property, though vacant, isn't actually abandoned by the title holder could put you in a difficult position. Speaking to an attorney who understands this area of law is very important.
This is not intended to be legal advice or create an attorney-client relationship. If more information is needed, you should consult with an attorney in your state regarding the specifics of your situation and the options available to you.