Since there is no ownership relationship between any of the ball companies you mentioned and Bowlmor, I would say no.  The AMF name is licensed by 900 Global which is the only relationship that exists.

I'm told the ball manufacturers must pay a $300k product registration fee. That doesn't include any of the other stuff they've got to pony up. And that product registration fee is something the PBA desperately needs coming in to keep the doors open.

I guess it depends on how you look at it. How much do these companies spend on advertising in a year? I can't speak for the companies mentioned in the OP, but Brunswick has a full page ad, usually on the back cover or inside front cover of the Bowler's Journal every month (or at least they used to). That is prime real estate and very pricey. The PBA registration fee is nothing more than additional advertising. If you have good equipment and you have good bowlers, your product gets on TV and seen by the public. With Sean Rash, Tom Smallwood, Parker Bohn,and Jason Sterner (all that I can think of at the moment) on their roster, there is a good chance Brunswick will be on TV quite a bit. Look at Motiv during the Summer Swing, I bet they saw some pick up with Ronnie Russell winning and E.J. Tackett making some shows. It's all a matter of perspective.
 
But, that being said, the companies in the OP are much smaller then Brunswick and potentially Motiv now. They also have had some financial issues, when it comes to 900Global/AMF. So they may not be able to justify that kind of advertising expenditure. Maybe with Storm's infusal of cash into Global900/AMF, they might all extend that to include PBA registration, I guess we will have to wait and see.

It's all about cost-benefit analysis. PBA shows have very little visibility anymore. It was different way back when the Tour was on network TV every Saturday morning and had a large following. These days the shows are taped and rebroadcast on ESPN in a time slot that competes with NFL football and other more popular sporting events. As such, there are fewer and fewer people even watching the shows, so that means a lot less benefit to worrying about whether X-pro or Y-pro is using your stuff on that show. I'm sure there was a time when pro shop owners routinely had people coming in asking about this ball or that ball that they saw being used on the show, but I think those days have largely passed. As such, I just don't see any of the companies that have dropped registration picking it back up. It's just not worth the extra $$.

Gene and Joe,
     You are both correct. There may not be a valid benefit for the costs of being PBA registered. The only one I see potentially coming back would be 900Global, if Storm wants to put up the money to get the brand moving since they now have financial interest in it.

S-70,
   The AMF Bowling Balls are not associated with Bowlmor/AMF in any way. Bowlmor has nothing to register. 900Global owns the rights to the AMF300 bowling ball line. I would assume if Storm decides to register 900Global, or provides the financial backing to do so, then the AMF300 line would also be registered as part of that.

This is just like if/when someone buy Brunswick bowling balls. Bowlmor will have no association with that company and will not be involved in if that company keeps Brunswick bowling balls PBA registered.