Does saying 我今天26岁 imply it's my birthday today?
'我今天26岁' seems very strange to me, but it does transmits the sense that today is the birthday.

If you would like to imply that it is your birthday today, a more proper expression could be '我今天26岁了', where '了' puts in a sense of completion or perfectness so that the sentence would imply 'I turned 26 today', thus revealing that today is the speaker's birthday.

If you simply want to tell your age, '我今年26岁' would seem more natural to native Chinese.