Highly doubt the X will need a new line for technical or engineering reasons other than 'we are making too damn many S's' or another way to say it is 'we've gone to Plaid, we can't slow down!!!'. So logistically, it might be an issue, but I'd bet they will run the line hot until the demand is satiated in EU and Japan then take over parts of the line as needed to make X parts and iterate. The robots can switch duties on a dime, switch out heads and do very different tasks so I don't expect they would take a throughput hit to iterating on X during S production to a large extent.
One reason that I see an AWD (aka front motor S) due out prior to showing the Beta X is that they will want to get a good understanding of how the new AWD assembly is implemented. Reason being is that with the Beta they will most likely start stating some technical details of the car beyond what has already been stated. These numbers won't be possible without a good working knowledge of how the AWD drive function will be implemented.
One piece of the puzzle that is very different for X will be the assembly of the Falcon doors which will most likely require at least one more station (two robots), maybe not immediately, but to keep up throughput, and with all the space they have, to keep quality high, iterate quickly...yata yata, it just makes sense. I could see Beta X's all making it down the line without any defects and then spending days trying to get those doors working properly. At TESLIVE I had a chance to study the current design/implementation of those doors and it looks to be a daunting challenge to not only get them functioning properly, make them safe under all conditions, air bags, two different actuating windows and four hydraulic hinges, but thing has got to work well. Not like the current handles well either. These doors are going to weigh quite a bit (100+ lbs) and there won't be any forgiveness if one fails or misbehaves in any way, shape or form. They must be flawless.
Some has said that the chassis might have different dimentions and this is most likely the case to establish an overall greater footprint, but I could see the X use the same chassis and still garner more space due to learnings with the current chassis and just moving the axels further forward and backwards to get that bigger footprint. TM knows they can pass the crash tests with the AWD (NOTE: They must already being doing this now to make the timelines) so they can take a bit of risk and push the envelope a bit. Not to mention the bigger tires gives them a bit more room on the Y-axis as well to improve upon cubic feet.
Ok, now I'm rambling...