Calculate Total Visits
There are a lot of questions and articles about packing time intervals. For example, Packing Intervals by Itzik Ben-Gan.

You can pack your intervals for the given user. Once packed, there will be no overlaps, so you can simply sum up the durations of packed intervals.



If your intervals are dates without times, I'd use a Calendar table. This table simply has a list of dates for several decades. If you do not have a Calendar table, simply create one:

CREATE TABLE [dbo].[Calendar](
    [dt] [date] NOT NULL,
CONSTRAINT [PK_Calendar] PRIMARY KEY CLUSTERED 
(
    [dt] ASC
));


There are many ways to populate such a table. 

For example, 100K rows (~270 years) from 1900-01-01:

INSERT INTO dbo.Calendar (dt)
SELECT TOP (100000) 
    DATEADD(day, ROW_NUMBER() OVER (ORDER BY s1.[object_id])-1, '19000101') AS dt
FROM sys.all_objects AS s1 CROSS JOIN sys.all_objects AS s2
OPTION (MAXDOP 1);


See also Why are numbers tables "invaluable"?

Once you have a Calendar table, here is how to use it.

Each original row is joined with the Calendar table to return as many rows as there are dates between StartDate and EndDate.

Then we count distinct dates, which removes overlapping dates.

SELECT COUNT(DISTINCT CA.dt) AS TotalCount
FROM
    #Items AS T
    CROSS APPLY
    (
        SELECT dbo.Calendar.dt
        FROM dbo.Calendar
        WHERE
            dbo.Calendar.dt &gt;= T.StartDate
            AND dbo.Calendar.dt &lt;= T.EndDate
    ) AS CA
WHERE T.CustID = 11205
;


Result

TotalCount
7