No, you cannot park overnight at Welch. This is a river access point with no camping posted. You may however, wander off at least 50 ' from the access point to be considered in the national park. What land area can be considered Welch access point is the question. I would consider the trail to the spring, the parking lot, and the road that does just downstream of the access point all part of the no camping area.
When I camp there I put everything in my canoe and drag it upstream to the nice gravel bar.
Kip