I don't own either but I can make a stab. I use these Amazon review and questions.
In descending order of most important 1st.
1) Voltage. No matter anything else, if its not the minimum voltage, it can never charge the Powerhouse.
From the comments, if you take the PSU supplied of the Powerhouse you see a 16V-17V input.
Looking a the GoalZero Boulder 50 specs:
I see an open circuit voltage of 18V-20V. However a closed circuit voltage is often lower, so its already showing borderline acceptability. However 18-20 > 16-17 so it passes that check.
2) port shape.
From the review and Anker's replies here
I see "is a round cable with below tip size: 7.5mm*4.8mm*0.7mm"
How does that compare with "8mm" ? It is not strictly the same right? Might fit, might not. But 7.5 != 8 therefore its got signs of not working.
3) Watts. I see a claim of 50W. A quick search of reviews don't show actual Watts but the review implies it is at least 50W
So then let's do the math. 50W so over a sunny day if you just pointed the Goalzero tilted to the latitude and season to be average at the sun then you'd get about half the daylight hours, so say 6 hours equivalent in good conditions. 6x50 = 300Wh. The Powerhouse is 434Wh so you're looking at about 3/4ths of a full recharge in a good day.
The caveats would be: would the pin work? If in less than ideal situations what happens, does the voltage drop? If so how less than perfect is it before it drops so low it stops charging? You could in cloudy conditions get no power whatsoever all day.
To help solve this puzzle, do you own a meter which can measure voltage? Do you have anything (not Powerhouse) which can act as a closed circuit drain? Connect all 3 items and measure, what is the voltage in different conditions? If its >16V you're in with a reasonable chance. Might need to make up a special adapter. The Amazon reviews show solar panels with adapter kits for the pin shape.
I don't see a regulator mentioned in the Boulder specs, this Q&A implies none.
What a regulator would do is step down amp and up volt to maintain a minimum voltage, that would make the panel less useless in less than perfect situations. So if you find you're getting <16V then consider some kind of regulator. Also if the Boulder were to get >17V unregulated, it risks burning the Powerhouse (its upper tolerance I do not know but its a warning).
In the Anker solar panels there is a regulator to output 4.2V-5.1V in the range to be above minimum for USB standards, so you'd probably need equivalent for the Powerhouse minimum input if the Boulder's voltage varies too easily <16V or >17V.