Sure you can but, why would you want to especially considering the galvanic corrosion potential when joining or even mating the two different metal's own "Noble" numbers which would guarantee galvanic corrosion, and even other types of corrosion to occur in rather short notice??? If you could give us more details, maybe we could offer some suggestions. ;)
Respectfully,
Henry

A7 steels were required to meet tensile and yield strength requirements. Chemistry was not controlled for weldability, thus some heats are easily welded while other heats contained sufficient sulfur, phosphorus, and carbon to be difficult to weld.

An easy means of assessing the weldability of the A7 you are working with is to use a single pass fillet weld to secure a piece of 1/2 X 4 X 6 plate to the A7 bearing block. Strike it with a sledge hammer to see if it tears out of the A7 or fails through the throat of the fillet weld. If it fails by tearing out of the A7, you have a pretty good idea that there may be some problems.

It is always better to send a small piece of the bearing block out for a chemical analysis if possible, but sometimes it isn't practical.

You can consider using a transition layer (butter layer) of E7018-H4 (Lincoln Excalibur) with high manganese content and then weld the stainless steel block to the layer of E7018-H4. The E7018-H4 will tolerate the low melting point constituents (in the A7) better than any austenitic stainless steel filler metal. Most manufacturers produce several electrodes meeting the E7018 requirements. Some contain higher manganese than others. In an application such as this, I prefer the high manganese to counter the affects of sulfur. So, be picky when selecting the "brand" you use.

You do need to know what austenitic stainless steel alloy you are welding. Depending on the thickness of the ASS, you might want to use a transition layer of E309-15 followed by an EXXX-16 stainless filler metal due to availability and weldability issues.

Even if chemical analysis indicated the existing bearing blocks are A36, you should use 309 to join the ASS to the carbon steel.

Welding should extend "all-around" to make sure moisture will not get in between the carbon steel and stainless steel and present a corrosion problem as suggested by Henry. Likewise, the paint system should extend up to the stainless plate (over the weld deposit) to prevent any galvanic action between the CS and the ASS.

Given the limited information provided, that's about all I can suggest for your consideration.

Best regards - Al