I am trying to convert some points from NAD27 Lambert Conformal Conic (custom projection) to WGS84 using QGIS 2.8.9. I am using the datum transformation parameters for El Salvador published here: http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
I have created a custom projection using the following proj4 string:
+proj=lcc +lat_1=13.31666666 +lat_2=14.25 +lat_0=13.78333333333333 +lon_0=-89 +x_0=500000 +y_0=295809.184 +k_0=0.999967040 +datum=NAD27 +ellps=clrk66 +units=m +no_defs +towgs84=0,125,194,0,0,0,0
It seems the +towgs84 parameters are not being applied. If I drop the +datum=NAD27 it seems it works. I have seen this suggestion in On the fly transformation From WGS84 to NAD27 with proj4 code, but I don't understand why it works. According to this in Reprojecting between NAD27 and WGS 84 part III, the +datum=nad27 parameter overrides the +towgs84 parameter, so I can use only one of them.
So my question is, can I specify a datum and some transformation parameters to WGS84 in proj4, or I just need to specify the ellipsoid? (Although it's an ellipsoid, not a datum)

+datum=nad27is expanded internally as ellipsoid and conus grid file. You only can use the first one, and need the +towgs84 parameter instead of the second. ARCGIS handles datum shifts differently, so you are better off with a custom CRS. But always check that QGIS uses that, and not the standard EPSG code. – AndreJ May 10 '16 at 13:32