We use radial velocity (RV) observations to search for long-period gas giant companions in systems hosting inner super-Earth (1-4 R ⊕, 1-10 M ⊕) planets to constrain formation and migration scenarios for this population. We consistently refit published RV data sets for 65 stars and find nine systems with statistically significant trends indicating the presence of an outer companion. We combine these RV data with AO images to constrain the masses and semi-major axes of these companions. We quantify our sensitivity to the presence of long-period companions by fitting the sample with a power-law distribution and find an occurrence rate of 39% ± 7% for companions 0.5-20 M Jup and 1-20 au. Half of our systems were discovered by the transit method, and half were discovered by the RV method. While differences in the RV baselines and number of data points between the two samples lead to different sensitivities to distant companions, we find that occurrence rates of gas giant companions in each sample are consistent at the 0.5σ level. We compare the frequency of Jupiter analogs in these systems to the equivalent rate from field star surveys and find that Jupiter analogs are more common around stars hosting super-Earths. We conclude that the presence of outer gas giants does not suppress the formation of inner super-Earths, and that these two populations of planets instead appear to be correlated. We also find that the stellar metallicities of systems with gas giant companions are higher than those without companions, in agreement with the well-established metallicity correlation from RV surveys of field stars.