On the 757/767 we operate, We have auto climb thrust enabled on most of the fleet.
In the case of a low level ALT CAP we can use any of the following, depending on what we want to achieve.
1. VNAV
2. FL CH
3. CLB Pwr, set desired speed in MCP window, then SPD.
As far as low speed protection applying I have never been that far back down the speedtape to have worried about it. However, proper briefing when this is likely to occur will bring it to both pilots attention.
One method I occasionally use in the event of a Low Level ALT CAP occuring is to select VNAV at a lower than 'normal' height. Our standard accel alt is 1500'aal, but going out of Orlando for example, where an iniial clearance is to 3000ft, I will brief the selection of VNAV at 1000'aal to avoid said problem, most trainers I have flown with are fine with it and it has never been criticised before.