Well, it's not out of the question. Less likely when they look at the reality of the situation though. The rental market in a lot of places has shrunk considerably because many BTL landlords sold up during the housing stampede last year. So getting a rental in itself could be tricky- do you know if they have pets?- that makes them less attractive.
The hassle of moving twice is also a big no-no to some people. Two lots of packing up and cleaning to a sparkly finish in a short space of time can take it out of some people. Bigger rentals command huge premiums these days, so if they go somewhere smaller, they might begrudge the storage fees for their stuff.
We did it, moved into rented (and we're still here- sob!). So it does happen. But you might need to gauge how motivated these vendors actually are. If all else fails and they seem to be wavering closer to your hoped-for moving date, you can offer a cash incentive (pay a set fee towards removal fees or storage costs for a set time- can be left with the solicitor).
Conveyancing also seems to have slowed down for all but the most simple transactions or insistent buyers and vendors. Make sure you've set out how regularly you want a progress report from the solicitor (weekly is fine, don't expect anything on a Friday, the country is obsessed with Friday completions). Make sure you ask if there's anything else you need to be pushing the vendors for (outstanding documents or replies to enquiries usually). Then go through the estate agent if possible, just explaining that "The solicitor says we are waiting on _, do yo know if it's been passed to their solicitor yet?" Estate agents are usually motivated because if the sale doesn't complete, they don't get their money.
You also need to work out how mentally prepared the vendors are. If you push too much, they may have a meltdown. Hopefully, you've found some robust individuals, genuinely looking towards their next stage. Good luck!
This is obviously independent of any mortgage you might have set up, so it needs writing into the contract and has to be funded by yourselves. Your solicitors would be able to advise.