Yes, I played one of my own pieces for Trinity Grade 6 last year in Australia. I got 21 out of 22 for it, so it didn't do me any harm!
Trinity build in this option for a reason (to encourage creativity and to allow a more R-brained, less prescriptive approach to exams and music in general, I would suggest!) There is no reason why you shouldn't do it, in fact you are likely to get a positive response from the examiner for having the gumption to do so. So go for it!
I would recommend having a close look at the syllabus to check the regulations and to ensure your piece complies with them, including length. From memory they give you some themes to write a piece around, although you don't have to use them. Your piece needs to equate to the grade you are doing in terms of difficulty. I would stress the importance of your score - you are required to hand over a copy and it goes without saying that it needs to be 100 % accurate and correctly express the rhythm, dynamics, voicing etc.
I had no special reason to do an exam. Having had a terrific teacher in Sydney, I moved up here to a country area 2 years ago. Just to keep my interest up (now being a little isolated) and simply to find out what doing an exam was like, I decided to do one. I could have taken AMEB or Trinity. I found the Trinity syllabus friendlier both in terms of the choice of pieces and in being somehow less didactic. I write lots of music, so loved the option of playing one of my own pieces. Also, I could do the exam on the Gold Coast, only 25 minutes away. The local Trinity contact and visiting examiner were both really friendly and encouraging. I could not speak more highly of the Trinity experience.
Good luck, let us know how it goes