tl dr: My best guess is, the battery should fully recharge the power station and still start your vehicle.
NOTE: If you are going to use your 26AH power station as a source of juice, wouldn't you be doing that while the vehicle is off and recharge it when it's running? Wouldn't this negate all of this arithmetic? At least, that's the way I'd utilize it. Provide power while the vehicle is shut off and recharge it when it's running. You'd no longer have to worry about whether your vehicle battery can handle it or not ... it would just work.
I can answer part of your question, the rest I will surmise.
... my battery is 140 minute reserve AGM can it fully charge a 26AH lithium battery from empty while idle ...
The answer to this is yes, it can. Here's how the conversion works for reserve capacity to AH:
Multiply the reserve capacity by 60 to convert it to seconds. For example, if a battery offers a 100-minute capacity: 100 x 60 = 6,000 seconds.
Multiply this length of time by 25, which is the battery's amperage. Example: 6,000 x 25 = 150,000. This is the number of coulombs of charge in the battery.
Divide this answer by 3,600, which is the number of coulombs in an amp-hour. Example: 150,000 / 3,600 = 41.67. This is the number of amp-hours in the battery.
TIP: To convert in a single step, divide the reserve capacity by 2.4
In your case, you have 140 minute reserve capacity. Divide this number by 2.4, which equals 58.3AH. That is more than enough to charge your 26AH power station. If there was a straight 1:1 charge ratio (taking 26AH from your 58.3AH battery), then you're taking almost 1/2 of the capacity of the battery to charge the power station. If you consider how the reserve capacity of a battery is figured, the formula is:
... the number of minutes a fully charged battery at 80°F will discharge 25 amps until the battery drops below 10.5 volts.
A fully charged battery should be around 12.7vdc. At 80°F, if you discharged your battery at 20A, you could expect it to last 140 minutes, at which point it would be 11.9vdc, which is considered fully discharged. The same website also states:
... it's very important to know that the total time of discharge and load applied is not a linear relationship. As your load increases, your realized capacity decreases. This means if you discharged that same 100 AH battery by a 100 amp load, it will not give you one hour of runtime. On the contrary, the perceived capacity of the battery will be that of 64 amp hours.
I can only take this to mean the inverse must also be true, that being, if you are utilizing an amp draw below 20A, your reserve time must be increased non-linearly. This will help you somewhat, as I would have to assume the power draw is going to be much less than 20A.
Then there is also the conversion factor of your device, which means, it will deplete more power than it will put back into your power station. As a rough estimate, I'd suggest it would probably be around 10% (I think this is a safe guess). To fully charge the 26AH power station, you'd use about 28.6AH out of your battery, which is well beyond the 1/2 way point of your battery. If we looked at it directly of 1/2 of the charge between 12.7v and 11.9v would be 12.3v. This should be enough to start your vehicle.