No, it would not be considered "forced overtime" that requires time-and-a-half. The hours that put you into overtime are actually worked hours. So for example, if you only still work forty hours in that week, the employer does not have to pay OT rate for the 8 hours or so you work on the fifth (the employer only needs to pay you for working those 8 hours and can also pay you the 8 hours of holiday).
I fear I'm not explaining this well, so let me give another example. I was a controller for an MRO facility. Some of our airplane mechanics would play games and call in paid sick time for two days and then work forty hours later on in the same week. While their total pay would be 56 hours for the week, we were not required by law to pay an OT rate for the extra 16 hours.
Now, your employer may choose to be very generous and give you 1 1/2 time for working on the company holiday, but that is the employer's choice. When I waitressed through college, I worked many a paid holiday (and I consider myself lucky that we restaurant workers were even given paid holidays). One restuarant I worked at gave us 1 1/2 time plus the holiday pay (so 2 1/2 -- plus people tip great on holidays out of pitty I guess -- although I always maintained a great attitude).