With the impressively expanded serial number page for Remington at the typewriterdatabase, there are monthly serial numbers for some of the portable machines. E.g after September 1928, there is a consecutive serial numbering for the Remington Portable typewriter, a type that is advertised as a Christmas gift.
To what extent was the portable typewriter actually a gifting item then at that time. Did the boy indeed get it? If the portable typewriter was significantly a gifting item, then there should be some visible seasonality in the production numbers.
Taking the serial numbers for the Remington Portable from the database and plotting the size of the monthly blocks as a volume yields the graph below. This suggests that at least for 1929, the monthly increments were done by choosing every month a starting number. The monthly volumes are suspiciously nicely rounded numbers; 1000 or 1100. After summer 1930, the numbers start to suggest consecutive numbering, i.e. they probably more closely represent monthly production volumes. (The sharp drop in block size in the summer of 1930 is a bit too late to attribute it to a likely sharp drop in volume sold after October 1929.)
Looking at the overall chart, there seems to be no clear annual pattern in production volume.
Even when allowing for a longer time from manufacture to actual consumer purchase than there is today, this would surely not be longer than 12 months. The distribution and warehousing also then would have been able to route a machine to the purchaser within no more than a few months. A typewriter was too expensive an item to make to stock, would take up too much capital.
There is perhaps a suggestion in the graph that most are produced in the first half of the year. That could then mean that time from production to sale was around 6 months and the majority of machines is sold for Christmas. An alternative explanation would be the start of the school season being a driver for purchases, with a couple of months lead-time from production to purchase.
The numbers for 1933 however are concentrated in the second half of the year, making it less likely that there really is an annual pattern. Also the volumes become relatively small after 1931 for this type. Overall the graph does not give much insight into the effect of advertising the machine as a Christmas gift. It looks a bit random. At most it could be concluded that there is no clear indication of seasonality in the serials for the #2 and #3 Portable.
With the #2 and #3 numbers trailing off, perhaps another machine would be likely to be a home gifting item. E.g. the Compact Portable of that period. Taking its monthly serial numbers from the database and plotting the size of the monthly blocks gives the graph below.
Ergo the gifting of a typewriter for Christmas may have caused a surge in sales for Christmas, but the monthly serial number blocks do not show effect of this in annual production patterns.
Not sure if the boy did get it...
(A very impressive resource is the typewriterdatabase. As already remarked by Ted upon his expanding the Corona page, the data can contain answers and hints for many more and more varied questions than the dating of a machine.)