May an LLC receive gifts in a similar fashion as a non-profit organization?
An LLC may receive gifts as any other entity. I assume you are asking whether a gift to a charitable LLC is deductible as a charitable contribution. If the LLC has obtained its own recognition of exemption under Section 501(c)(3), the answer is Yes. (See Ready Reference Page: "LLCs Becoming Entity of Choice for Subsidiaries.") If it is a single-member LLC of which a charity is the single member, the LLC is "disregarded" for tax purposes. By all logic, a gift to such a "disregarded" entity should be treated as a gift to the parent charity and deductible, but the IRS did not so rule until 2012. The Service has now agreed that it should be treated as a deductible gift to the parent organization. (See Nonprofit Issues, 7/16/12.)
Finally, IRS recognizes deductibility of gifts to single member LLCs