Yes. The short cruise is a good idea. Not just for the discount, but for something far more important -- to see whether you actually like the ship, its atmosphere, activities, food, the personnel, etc. No one cruise line is right for everyone and there is nothing worse than three months of being on the wrong ship at these prices.
More to the point, whether this is the right ship and right line for your honeymoon (and congratulations!) is very much a personal matter based on what each cruise line offers and what it is you specifically want from a cruise. A few thoughts based on your post:
First, a short cruise will not give an accurate flavor of a longer cruise for at least two reasons. First, there will be far fewer port days and you will have to entertain youselves on board rather than exploring onshore. Ships are very different on the days that they are in port compared to sea days. Therefore, before booking a world cruise, be VERY careful to review the activities and amenities offered by the line to see if they are to your liking - including lecturers, musical programs, entertainers, etc. Obvious example, don't expect any rap music on board; do expect a fair amount of big band.
Second, the passenger profile on a world cruise is very different fromt he short cruises. You will be among the youngest (if not the very youngest) passengers on the ship. I would estimate the average age at about 60 for most of Radisson's cruises. It is easily above 75-80 on the world cruise. (The longer the itinerary, the older the average passenger.) Radisson's passengers are generally well-heeled business people, mid to late career professionals, and retired persons. This profile will be reflected in the types of shows and performances put on, the lecturers and the subjects of their lectures, the music played in the lounges and for dancing, etc. To the extent that you want to participate in shipboard activities, make sure that you find out the activities that the ship offers and whether there are activities of interest to you. The activities, lecturers, shopping, etc., on Radisson will reflect the likes and wants of this clientele, not generally of the younger generations.
Keep in mind that, especially on world cruises, Radisson really does not market itself to younger passengers or to honeymooners. A world cruise does not provide a cruise experience geared toward honeymooners. I am told that there is now a honeymoon package available for $300.
From your comment about "refined experience," I assume you mean things like food, entertainment, and shopping. Radisson's onboard shops are more high end than the mass market ships and the prices are high end as well. Radisson's food is better than the mass-market lines with a decent variety on the menu. While it is usually well-prepared, in my several recent Radisson cruises, I have experienced too many lapses in preparation for a luxury line (yolks cooked solid in eggs benedict, 25 minute wait for service, etc.). The free wine with dinner does not make up for these deficiencies. I was not impressed with Voyager's specialty restaurant Signatures on my last cruise (a segment of a world cruise). If you are gourmands or are looking to treat yourselves to a really first-class dining exprience, you should look into Crystal, Seabourn, and Silversea. The food on each is definitely superior to Radisson's - and this is particularly true as between Radisson's and Crystal's specialty restaurants. (There are some specials on Crystal that bring its prices fairly well into competition with Radisson.)
Select your cabin on the basis of the amount of time you plan to spend in it and your own personal need for space. Nothing worse than paying for the most expensive cabin on the ship and then using it only to sleep. Prabably, you would need at least the minimum penthouse because of space considerations and the amount you would take with you. On Voyager, by the way, do not get a cabin aft of midships, even though some people say it is enough to be forward of the laundry rooms. Voyager has had a definite vibrarion problem in the aft prt of the ship (and I am told it is worse at higher trans-oceanic speeds on the world cruise) and I have not heard that it has been fixed.
Finally, be sure to consider your own personal wants and needs. Several rather obvious examples: (1) If you like wine with dinner, Radisson provides wines (included in the cruise price) that are quite good. f you do not like to get dressed up for dinner or for the evening and if you do not like, at least, "country club casual" for the daytime on a world cruise, then do not even consider Radisson.
Hope that some of this will be of help to you.