Having completed a FAA 737 NG Type Rating earlier this year I thought I would reply to your post.
I think it would be possible to complete a type rating in this time but there a several factors that could influence the outcome.
Your system and procedural knowledge will have to be 100% from the first session. The amount of flying hours you have, your instrument skills and currency will also impact your progress. A Jet transition course before the type rating would be a huge help.
Your sim partner’s competence (see above) will also have an effect on your progress.
If any of these factors aren’t on your side you may need extra training, I think Boeing in Miami charge around $700 per hour
for the NG sims just FYI.
Anyway I hope this helps !