Most pumped systems do when they discharge into a stack pipe. I have never seen sewage coming out of the top of a soil stack where a pumped system has been involved. That said where a pumped system discharges into a manhole ( inspection chamber ) whch has a lateral 100 mm pipe to the sewer some care has to be taken with the benching ( bottom of the chamber ) to reduce the amount of splashing that occurs.
No, but you're asking it to pump into a larger pipe, for it then to find its way back out and to the stack by gravity. Bear in mind what it is these things are pumping, and the size of the pipework involved. The Manufacturers instructions clearly state how the discharge pipework must be arranged, and any attempt to alter, deviate or ignore these instructions is promptly going to invalidate the warranty, at the very least.
Secondly, a poorly fitted lateral into a chamber, particularly from a WC, can cause fouling of the opposite benching, which is the reason care must be taken when laying drains to avoid this scenario if at all possible.
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