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As I recall, transformers are made with short circuit characteristics in mind. The no-load current (I presume you mean primary current when there is no load on the secondary) may provide some insight into the transformer characteristics.
The influence will be very small in a normal transformer. One way to represent a transformer is shown below. L1 and L2 are small and L3 is large, so the short circuit current will be very much larger than the no load current.
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