So what your saying is the 3.7v lipo will work to keep the realtime clock but the on board hardware will not be able to charge the battery to keep it in it's normal operating range, with a lipo that could mean a fire. That is if the battery voltage drops too low then is charged again. 
I have two questions. First is what type of charge management is provided? it would seem with just a flat 3.2 present when the main batt is above 3.2 would suggest that a ni-cad would be best suited. 
Second, can you provide the full link to the swcu50d.pdf you mention?

> From: lists@ssc-solutions.dk
> To: gumstix-users@lists.sourceforge.net
> Date: Thu, 5 Nov 2009 23:55:18 +0100
> Subject: Re: [Gumstix-users] Battery management
>
> Hi Kirk,
>
> Great news - Though one comment on the 3.7V battery for supplying the
> VBACKUP pin.
>
> Normally this pin is intended to be connected to a (rechargeable) backup
> battery on which it have the ability to charge when the main battery voltage
> is above 3.2V.
>
> The charger is able to charge the battery up to a voltage of maximum 3.2V
> (See swcu50d.pdf - Table 7-86), so applying a 3.7V input to the pin is
> definitely higher than what most designs do.
>
> I don't think it will cause you any problems though (since the pin just
> connects to an internal LDO and a resistive divider) but just asking you to
> keep in mind that applying a voltage larger than 3.2V might not be the best
> tested combination - Though it's working with your setup.
>
> Great news - Keep up the good work and keep us posted
> Søren
>
> ---
> SSC Solutions ApS - Denmark - www.ssc-solutions.dk
>
>
> > -----Original Message-----
> > From: Kirk Martinez [mailto:km@ecs.soton.ac.uk]
> > Sent: Thursday, November 05, 2009 4:31 PM
> > To: General mailing list for gumstix users.
> > Subject: Re: [Gumstix-users] Battery management
> >
> > out of interest I just put a 3.7V bat onto the VBACKUP pin-12 on the
> > Summit and powered-off the main unit completely... on repower the RTC
> > is
> > there and fine! The hwclock is read by a boot-time script automatically
> > so the real time/date is not lost.
> >
> > now to see if anyone has sample code for sleep/standby/apm stuff.....
> > Kirk
> >
> > R. P. McMurphy wrote:
> > > The Overo boards do not support battery charging. The circuitry is
> > not
> > > connected to anything usable.
> > >
> > > But you can directly power the Summit with a Li-type battery. The
> > > onboard regulator will run down to ~3.4V input and still maintain the
> > > 3.3V to the Overo.
> > >
> > > On 10/6/09, No <serge@navigator.lv> wrote:
> > >> Hi list!
> > >> Anybody know how to arrange LiPo backup battery with Gumstix
> > Overo+Summit
> > >> board. Is there possibility for correct automatic charging and
> > maintenance
> > >> for battery? I guess, the processor chip has battery management
> > module, but
> > >> do how I can use it?
> > >> Serge Batov.
> > >
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