I would say it would do a decent job. But IMO portable amps should be used to drive portable headphones like Koss porta pro/KSC-75 or for IEMs. The Shure 840 doesn't require a lot of power but a desktop amp will IMO do a better job at driving them.
Regarding your query on whether the amp will improve the sound or not, then you should know that your ipod and your laptop sound card already have an amplifier built in. However since the inbuilt amplifiers are not very good it may not be driving your Shures adequately.
Different headphones behave differently when driven by inadequate amplifiers but generally there is a very noticeable difference in SQ when the headphone is properly amped. So with the Ibasso D2+ acting as an amp, your Shures will be driven much better that and you may notice an slightly more enhanced soundstage and better bass. However do note that since the Shures are closed phones you will never get a very wide soundstage.
However the D2+ also acts as a DAC and it can replace your laptop sound card leading to further improvement sound as the Ibasso D2+ should have a better DAC than your laptops onboard sound card. However you cant use the DAC function with your ipod.
) ... I think the D2+ Boa will be the best option to drive both the IEM's and closed cans. 
