建议LZ直接问南航，或者乌鲁木齐边检。
按照最新的情况来看，去格鲁吉亚，无签证护照是放行的。
转自刘总博客
http://www.tmtravelworld.com/
中国因私护照白本可出中国边检的免签落地签国家
亚洲： 韩国的济州岛，印度尼西亚，马尔代夫，塞班
欧洲：格鲁吉亚
非洲：毛里求斯, 塞舌尔
大洋洲：斐济，帕劳, 瓦努阿图，密克罗尼西亚联邦， 图瓦卢
IATA资料显示可以落地签，没有提到什么邀请函。
Georgia (GE)
Passport required.
- Passport and/or passport replacing documents must be valid
for three months beyond the period of intended stay.
Visa Issuance:
Visa required, except for Holders of normal passports issued
to nationals of China (People's Rep.) can obtain a visa on
arrival.
Fee: GEL 50.- for a 90 day, single entry visa; GEL 100.- for
a 360 day, multiple entry visa .
Minors:
- Minors up to/incl. 15 years of age travelling alone must
hold either:
- passport; or
- letter of consent from the parents.
Additional Information:
- Passengers holding an open ticket, For details, click here