Only if it does 186-200mph in just over 1s. It should also be noted that the Weissach 918 measured on the same day took just under 30s and we've seen faster times for that. Conditions etc.
If you look at Autocar's quarter time, measured during the 0-200mph run, it hits 147.5mph in 10.2s, so the next 52.5mph to 200mph takes ~9.8s, or 0.98s for every 5.25mph assuming uniform acceleration (which is not the case due to drag depending on v^2). If you add 7 lots of that to the MT quarter time (9.8@149mph) you get 16.64s to 185.75mph. Again this assumes uniform acceleration, in reality the 150-186mph will involve faster acceleration than 186-200mph.
http://www.autocar.co.uk/car-review/mclaren/p1/performance
The factory claim is definitely reasonable and there's no reason to doubt it.