I haven't done this but I know several people who have, in various countries. There are certainly international schools which will avoid hiring staff with this qualification but there are many which are fine with it.
Which country are you in? Are you likely to stay there or move elsewhere?
As you're already in a school, I would ask if they would support you in terms of teaching practice even if you are self-funding. Don't put yourself on a course if you will then find it difficult to tick all the boxes for completion.
I have a colleague currently doing an international PGCE at my school. Her husband was hired as a teacher and she came on to do her training but she isn't paid at all. She is great though and the Head basically created a role for her next year, which will be properly paid. So it can work! We are in Thailand.
I also have a friend who moved to Latin America with her teacher husband and found it hard to get work in her field, so she did some TA work and showed potential and they supported her through her international PGCE. I don't know if she self-funded or if the school helped. But she went on to do very well and if anything has surpassed her husband in terms of career progression, despite being several years 'behind' him and with less 'impressive' qualifications. They have since moved to SE Asia without difficulty.
Definitely look into the course more if you're keen! You won't have your pick of every school moving forwards but there are plenty of doors open to you, and the more experience you get, the less the qualification/QTS status will matter. There are countries and schools you would have to knock off your list of possible employers though.
Good luck!