1A would be pushing it, yes. The AMC1117 is rated for 0.8A (max on a heatsink).
Note to others considering this repair: all of the following is somewhat sketchy, and best practice would be a small heat sink on this part, soldered directly to the board. It's my TV though

Using 0.8A as a worst-case current an AMC7588 in TO-263 with a 45ºC/W Tja is under Tj=150ºC even over 70º ambient with zero air flow. There is a small but perceptible convection current in there, and...
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