If your X data is evenly spaced, a category chart can still work for you. From your explanation, your data is every 7 days. As long as it is 7 days without fail, the result of a line (category) chart and scatter chart will be the same. If it isn't exactly 7 days once in a while, it might still be okay. Your call on that.
If column A has the dates for the X axis, the easiest way to make it use them as labels on a category chart (like the line chart) is to make column A a header column before making your chart. By default they will be used as the X axis labels.
One advantage of the line chart over the scatter chart is the X axis labels will be exactly the dates you have in column A. With a scatter chart, it will use dates that match up with the gridlines, which are unlikely to be the dates in column A.
To answer your direct question: yes, you can select the dates in column A to be the labels even if they are not in a header column.
- Don't select column A when making the chart
- Select the chart and go to the tab that has the X axis info
- Select all the "untitled's" in the Label References box and delete them
- While still in the box, select the range of cells from column A to use for the labels (or type it in)
- Set the Category Labels to "Auto-Fit" or to one of the other selections other than "none"