Tough to say without first hand knowledge but here's the info from the Glacier National Park Trail Status Page:
Logan Pass - Granite Park Chalet/ 7.6 mi.
Initial clearing scheduled for: 6/30/09. 256
Safety handline cable: Scheduled to installed 6/30/09. 256
Snow Cover: N/A
Trees Down: N/A
As long as snow conditions permit the trail could be good to go around the time you want to hike it or maybe the day after. Check before starting out though.
If it is closed the day you hike in perhaps you could hike in via the Loop then hike out to Logan Pass. All this assuming that the road opens across the pass as well.
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