doggin,
The short answer to your first question would be that, in IMHO the little SLA (sealed lead acid) baterry would NOT be a good choice for replacing the 8 D cells.
As to the second question, there are some things that we would need to know about the small SLA battery and the power consumption (watts or amp draw) of the caller to be certain about exactly how much longer the 8 D cells would run the caller. My reply above was just a ballpark estimate based on an average capacity value for the D cells. It could be more or less than the approx. 11 times that I calculated.
As best I can determine by doing some Google searches, lead acid battery capacities are based on a 20 hr discharge rate (I am not totally sure about this). That means that the little SLA above could provide a constant current of .065A for 20h (1.3Ah/20h=.065A=65mA). Looking at the specs for a Duracell D Cell on Duracell's website (http://www.duracell.com/oem/Pdf/new/MN1300_US_CT.pdf) shows that the 8 D's can provide a current of about .55A for 20h. I used the red line of the upper right graph on the second page to determine that value because it is the average of the three lines. Then, using the .55A value and looking at the red line on the middle left graph on the second page we can estimate a capacity of the D cells at about 12 Ah. That means that the 8 D cells could last about 9 times longer (12Ah/1.3Ah=9.23) than the little SLA battery. Lead acid batteries can, however, have their capacities improved if used intermittently (call for 30 min then go to the next stand 10-20 min away and call again). Here is a link that mentions something about that (http://www.batteryuniversity.com/partone-16a.htm). I am not sure if alkaline batteries do the same thing.
Even if the SLA battery's capacity was improved by intermittent use, I still think that we could safely say that the 8 D cells will last at least 5 times longer. In my opinion, that little SLA battery is just too small.