I don't have a spouse, much less an unaccompanying spouse, so I can't speak definitively on this matter, but...
I don't think they'll reject your profile if you simply edit it - a lot of people change their mind mid-way through the process about whether or not their spouse will be accompanying them because of a chance in circumstances.
*FYI, you wouldn't be applying as 'single' - you'd be applying as 'married with spouse not accompanying', but the points will be calculated as though you're single (but you'll still have to get a medical exam and PCC(s) for your spouse if you get an ITA)
The consequence would be that your spouse won't be able to come with you, and you'll have to be physically separated until you can sponsor them under the spousal sponsorship programme, which can take upwards of 12 months to be approved from the point of making the application...
Perhaps someone who is in this situation can advise a bit further - do you have to provide an explanation and affidavit as to why the spouse isn't accompanying you in situations like this? (And obviously you need to have a 'legitimate' answer, not "I realized it would increase my points and therefore my chances of getting PR"...