Is there a faster way to check if this is a valid date?

If your goal is to avoid using exceptions, you could write a custom validation method:

public bool IsValidDate(int year, int month, int multiplier, int dow)
{
    if (year < 1 | year > 9999) { return false; }

    if (month < 1 | month > 12) { return false; }

    int day = 7 * multiplier + 7 - dow;
    if (day < 1 | day > DateTime.DaysInMonth(year, month)) { return false; }

    return true;
}

This performs most of the same validations as the DateTime constructor you're using - it only omits the check to see if the resulting DateTime would be less than DateTime.MinValue or greater than DateTime.MaxValue.

If you mostly get good values, this would probably be slower overall: DateTime.DaysInMonth has to do a lot of the same things the DateTime constructor does, so it would add overhead to all the good dates.

String DateString = String.Format("{0}/{1}/{2}", model_.Date.Month, (7 * multiplier) + (7 - dow) + 2),model_.Date.Year);

DateTime dateTime;
if(DateTime.TryParse(DateString, out dateTime))
{
    // valid
}

As the comment pointed out by GenericTypeTea, this code will not run any faster than what you have now. However, I believe you gain in readability.