A residence permit and citizenship are different statuses with different rights. Owning property alone doesn't grant citizenship, but permanent residence can be a step toward it.
Standard route
Regular naturalization requires continuous residence in Georgia for a legally defined period (typically around 10 years), along with knowledge of the state language, history and basics of Georgian law.
Citizenship for special merit
The President of Georgia may grant citizenship without the usual residency requirement for outstanding contributions to the economy, culture, sport, or other service to the country. This is a discretionary decision, not a guaranteed process.
Dual citizenship
Georgia permits dual citizenship only in limited cases, mostly by presidential decision for naturalization on special merit — a typical applicant going through standard naturalization generally has to renounce their prior citizenship.
Practical tip
For most investors, a residence permit (see the article on residence permits) is a realistic and sufficient goal; treat citizenship as a separate question and consult a lawyer specializing specifically in this area.