I think it is perfectly fine, that is how i got my first career defining job. After 6 month of relevant experience, I landed a job in big company just like you described. I sent my resume to a vacancy which stated that required experience was from 2 to 3 years. I got the call and showed that I knew some things needed for the position and got the job.
So if you are good and willing to go the extra mile to learn something new and what is needed for company you are applying for, than why not. Most of the time the experience factor is to scare off inexperienced developers who are not sure about their skills. Because most of the time they need someone who can do the job and willing to learn something new to do it even better, not someone who have done something similar for few years and claims that he have the experience but can't do anything. This may not be the true for higher ranked positions, like managers or directors.
but would it harm any future attempts for other positions in the same company?
That depends what you actually tell about yourself, if its all true and you are competent, and did not get the job I really doubt that it can somehow impact applying for others jobs in that company. If you don't get the job, that does not mean that you are doomed. That means you did not get the job, that all. It completely different case if you mess up an interview badly, than it actually can impact further applications in that company.